id	sid	tid	token	lemma	pos
ejpam-6387	1	1	european	european	PROPN
ejpam-6387	1	2	journal	journal	PROPN
ejpam-6387	1	3	of	of	ADP
ejpam-6387	1	4	pure	pure	ADJ
ejpam-6387	1	5	and	and	CCONJ
ejpam-6387	1	6	applied	applied	ADJ
ejpam-6387	1	7	mathematics	mathematic	NOUN
ejpam-6387	1	8	2025	2025	NUM
ejpam-6387	1	9	,	,	PUNCT
ejpam-6387	1	10	vol	vol	NOUN
ejpam-6387	1	11	.	.	PROPN
ejpam-6387	1	12	18	18	NUM
ejpam-6387	1	13	,	,	PUNCT
ejpam-6387	1	14	issue	issue	NOUN
ejpam-6387	1	15	4	4	NUM
ejpam-6387	1	16	,	,	PUNCT
ejpam-6387	1	17	article	article	NOUN
ejpam-6387	1	18	number	number	NOUN
ejpam-6387	1	19	6387	6387	NUM
ejpam-6387	1	20	issn	issn	VERB
ejpam-6387	1	21	1307	1307	NUM
ejpam-6387	1	22	-	-	SYM
ejpam-6387	1	23	5543	5543	NUM
ejpam-6387	1	24	–	–	PUNCT
ejpam-6387	1	25	ejpam.com	ejpam.com	X
ejpam-6387	1	26	published	publish	VERB
ejpam-6387	1	27	by	by	ADP
ejpam-6387	1	28	new	new	PROPN
ejpam-6387	1	29	york	york	PROPN
ejpam-6387	1	30	business	business	PROPN
ejpam-6387	1	31	global	global	PROPN
ejpam-6387	1	32	the	the	DET
ejpam-6387	1	33	effect	effect	NOUN
ejpam-6387	1	34	of	of	ADP
ejpam-6387	1	35	variation	variation	NOUN
ejpam-6387	1	36	in	in	ADP
ejpam-6387	1	37	the	the	DET
ejpam-6387	1	38	order	order	NOUN
ejpam-6387	1	39	of	of	ADP
ejpam-6387	1	40	zeta	zeta	PROPN
ejpam-6387	1	41	function	function	NOUN
ejpam-6387	1	42	in	in	ADP
ejpam-6387	1	43	strip	strip	NOUN
ejpam-6387	1	44	(	(	PUNCT
ejpam-6387	1	45	0	0	NUM
ejpam-6387	1	46	,	,	PUNCT
ejpam-6387	1	47	1	1	NUM
ejpam-6387	1	48	)	)	PUNCT
ejpam-6387	1	49	on	on	ADP
ejpam-6387	1	50	the	the	DET
ejpam-6387	1	51	upper	upper	ADJ
ejpam-6387	1	52	bound	bound	NOUN
ejpam-6387	1	53	of	of	ADP
ejpam-6387	1	54	np(x	np(x	NOUN
ejpam-6387	1	55	)	)	PUNCT
ejpam-6387	1	56	zhwan	zhwan	PROPN
ejpam-6387	1	57	muhammed	muhamme	VERB
ejpam-6387	1	58	amen1,∗	amen1,∗	PROPN
ejpam-6387	1	59	,	,	PUNCT
ejpam-6387	1	60	faez	faez	PROPN
ejpam-6387	1	61	al	al	PROPN
ejpam-6387	1	62	-	-	PUNCT
ejpam-6387	1	63	maamori2	maamori2	PROPN
ejpam-6387	1	64	,	,	PUNCT
ejpam-6387	1	65	mudhafar	mudhafar	ADV
ejpam-6387	1	66	fattah	fattah	PROPN
ejpam-6387	1	67	hama1	hama1	PROPN
ejpam-6387	1	68	1	1	NUM
ejpam-6387	1	69	department	department	NOUN
ejpam-6387	1	70	of	of	ADP
ejpam-6387	1	71	mathematics	mathematic	NOUN
ejpam-6387	1	72	,	,	PUNCT
ejpam-6387	1	73	college	college	NOUN
ejpam-6387	1	74	of	of	ADP
ejpam-6387	1	75	science	science	NOUN
ejpam-6387	1	76	,	,	PUNCT
ejpam-6387	1	77	university	university	NOUN
ejpam-6387	1	78	of	of	ADP
ejpam-6387	1	79	sulaimani	sulaimani	NOUN
ejpam-6387	1	80	,	,	PUNCT
ejpam-6387	1	81	sulaimaniyah	sulaimaniyah	NOUN
ejpam-6387	1	82	46001	46001	NUM
ejpam-6387	1	83	,	,	PUNCT
ejpam-6387	1	84	iraq	iraq	PROPN
ejpam-6387	1	85	2	2	NUM
ejpam-6387	1	86	department	department	NOUN
ejpam-6387	1	87	of	of	ADP
ejpam-6387	1	88	information	information	NOUN
ejpam-6387	1	89	networks	network	NOUN
ejpam-6387	1	90	,	,	PUNCT
ejpam-6387	1	91	college	college	NOUN
ejpam-6387	1	92	of	of	ADP
ejpam-6387	1	93	information	information	NOUN
ejpam-6387	1	94	technology	technology	NOUN
ejpam-6387	1	95	,	,	PUNCT
ejpam-6387	1	96	university	university	PROPN
ejpam-6387	1	97	of	of	ADP
ejpam-6387	1	98	babylon	babylon	PROPN
ejpam-6387	1	99	,	,	PUNCT
ejpam-6387	1	100	babil	babil	PROPN
ejpam-6387	1	101	,	,	PUNCT
ejpam-6387	1	102	iraq	iraq	PROPN
ejpam-6387	1	103	abstract	abstract	NOUN
ejpam-6387	1	104	.	.	PUNCT
ejpam-6387	2	1	during	during	ADP
ejpam-6387	2	2	the	the	DET
ejpam-6387	2	3	third	third	ADJ
ejpam-6387	2	4	decade	decade	NOUN
ejpam-6387	2	5	of	of	ADP
ejpam-6387	2	6	the	the	DET
ejpam-6387	2	7	last	last	ADJ
ejpam-6387	2	8	century	century	NOUN
ejpam-6387	2	9	,	,	PUNCT
ejpam-6387	2	10	arne	arne	ADJ
ejpam-6387	2	11	beurling	beurling	NOUN
ejpam-6387	2	12	introduced	introduce	VERB
ejpam-6387	2	13	the	the	DET
ejpam-6387	2	14	generalise	generalise	NOUN
ejpam-6387	2	15	primes	prime	NOUN
ejpam-6387	2	16	as	as	ADP
ejpam-6387	2	17	any	any	DET
ejpam-6387	2	18	increasing	increase	VERB
ejpam-6387	2	19	positive	positive	ADJ
ejpam-6387	2	20	real	real	ADJ
ejpam-6387	2	21	sequence	sequence	NOUN
ejpam-6387	2	22	starting	start	VERB
ejpam-6387	2	23	with	with	ADP
ejpam-6387	2	24	a	a	DET
ejpam-6387	2	25	real	real	ADJ
ejpam-6387	2	26	number	number	NOUN
ejpam-6387	2	27	greater	great	ADJ
ejpam-6387	2	28	than	than	ADP
ejpam-6387	2	29	1	1	NUM
ejpam-6387	2	30	called	call	VERB
ejpam-6387	2	31	”	"	PUNCT
ejpam-6387	2	32	beurling	beurling	NOUN
ejpam-6387	2	33	primes	prime	NOUN
ejpam-6387	2	34	”	"	PUNCT
ejpam-6387	2	35	.	.	PUNCT
ejpam-6387	3	1	where	where	SCONJ
ejpam-6387	3	2	the	the	DET
ejpam-6387	3	3	fundamental	fundamental	ADJ
ejpam-6387	3	4	theorem	theorem	NOUN
ejpam-6387	3	5	of	of	ADP
ejpam-6387	3	6	arithmetics	arithmetic	NOUN
ejpam-6387	3	7	gives	give	VERB
ejpam-6387	3	8	beurling	beurle	VERB
ejpam-6387	3	9	integers	integer	NOUN
ejpam-6387	3	10	.	.	PUNCT
ejpam-6387	4	1	this	this	DET
ejpam-6387	4	2	work	work	NOUN
ejpam-6387	4	3	study	study	NOUN
ejpam-6387	4	4	beurling	beurling	NOUN
ejpam-6387	4	5	’s	’s	PART
ejpam-6387	4	6	prime	prime	ADJ
ejpam-6387	4	7	systems	system	NOUN
ejpam-6387	4	8	and	and	CCONJ
ejpam-6387	4	9	concentrates	concentrate	VERB
ejpam-6387	4	10	on	on	ADP
ejpam-6387	4	11	the	the	DET
ejpam-6387	4	12	upper	upper	ADJ
ejpam-6387	4	13	bound	bind	VERB
ejpam-6387	4	14	of	of	ADP
ejpam-6387	4	15	beurling	beurle	VERB
ejpam-6387	4	16	zeta	zeta	PROPN
ejpam-6387	4	17	function	function	NOUN
ejpam-6387	4	18	in	in	ADP
ejpam-6387	4	19	the	the	DET
ejpam-6387	4	20	region	region	NOUN
ejpam-6387	4	21	(	(	PUNCT
ejpam-6387	4	22	0	0	NUM
ejpam-6387	4	23	,	,	PUNCT
ejpam-6387	4	24	1	1	NUM
ejpam-6387	4	25	)	)	PUNCT
ejpam-6387	4	26	.	.	PUNCT
ejpam-6387	5	1	this	this	PRON
ejpam-6387	5	2	reflects	reflect	VERB
ejpam-6387	5	3	of	of	ADP
ejpam-6387	5	4	course	course	NOUN
ejpam-6387	5	5	on	on	ADP
ejpam-6387	5	6	the	the	DET
ejpam-6387	5	7	size	size	NOUN
ejpam-6387	5	8	of	of	ADP
ejpam-6387	5	9	the	the	DET
ejpam-6387	5	10	error	error	NOUN
ejpam-6387	5	11	term	term	NOUN
ejpam-6387	5	12	of	of	ADP
ejpam-6387	5	13	beurling	beurling	NOUN
ejpam-6387	5	14	counting	counting	NOUN
ejpam-6387	5	15	function	function	NOUN
ejpam-6387	5	16	of	of	ADP
ejpam-6387	5	17	integers	integer	NOUN
ejpam-6387	5	18	np(x	np(x	NOUN
ejpam-6387	5	19	)	)	PUNCT
ejpam-6387	5	20	.	.	PUNCT
ejpam-6387	6	1	2020	2020	NUM
ejpam-6387	6	2	mathematics	mathematic	NOUN
ejpam-6387	6	3	subject	subject	NOUN
ejpam-6387	6	4	classifications	classification	NOUN
ejpam-6387	6	5	:	:	PUNCT
ejpam-6387	6	6	11n80	11n80	NUM
ejpam-6387	6	7	,	,	PUNCT
ejpam-6387	6	8	11m32	11m32	NUM
ejpam-6387	6	9	key	key	ADJ
ejpam-6387	6	10	words	word	NOUN
ejpam-6387	6	11	and	and	CCONJ
ejpam-6387	6	12	phrases	phrase	NOUN
ejpam-6387	6	13	:	:	PUNCT
ejpam-6387	6	14	beurling	beurle	VERB
ejpam-6387	6	15	primes	prime	NOUN
ejpam-6387	6	16	,	,	PUNCT
ejpam-6387	6	17	beurling	beurle	VERB
ejpam-6387	6	18	integers	integer	NOUN
ejpam-6387	6	19	,	,	PUNCT
ejpam-6387	6	20	beurling	beurle	VERB
ejpam-6387	6	21	zeta	zeta	NOUN
ejpam-6387	6	22	function	function	NOUN
ejpam-6387	6	23	1	1	NUM
ejpam-6387	6	24	.	.	PUNCT
ejpam-6387	7	1	introduction	introduction	NOUN
ejpam-6387	7	2	the	the	DET
ejpam-6387	7	3	theory	theory	NOUN
ejpam-6387	7	4	of	of	ADP
ejpam-6387	7	5	numbers	number	NOUN
ejpam-6387	7	6	is	be	AUX
ejpam-6387	7	7	one	one	NUM
ejpam-6387	7	8	of	of	ADP
ejpam-6387	7	9	the	the	DET
ejpam-6387	7	10	important	important	ADJ
ejpam-6387	7	11	branch	branch	NOUN
ejpam-6387	7	12	in	in	ADP
ejpam-6387	7	13	mathematics	mathematic	NOUN
ejpam-6387	7	14	that	that	PRON
ejpam-6387	7	15	deals	deal	VERB
ejpam-6387	7	16	with	with	ADP
ejpam-6387	7	17	properties	property	NOUN
ejpam-6387	7	18	of	of	ADP
ejpam-6387	7	19	counting	count	VERB
ejpam-6387	7	20	number	number	NOUN
ejpam-6387	7	21	involving	involve	VERB
ejpam-6387	7	22	riemann	riemann	PROPN
ejpam-6387	7	23	zeta	zeta	PROPN
ejpam-6387	7	24	function	function	PROPN
ejpam-6387	7	25	.	.	PUNCT
ejpam-6387	8	1	analytic	analytic	ADJ
ejpam-6387	8	2	number	number	NOUN
ejpam-6387	8	3	theory	theory	NOUN
ejpam-6387	8	4	is	be	AUX
ejpam-6387	8	5	that	that	SCONJ
ejpam-6387	8	6	branch	branch	NOUN
ejpam-6387	8	7	of	of	ADP
ejpam-6387	8	8	number	number	NOUN
ejpam-6387	8	9	theory	theory	NOUN
ejpam-6387	8	10	which	which	PRON
ejpam-6387	8	11	deals	deal	VERB
ejpam-6387	8	12	with	with	ADP
ejpam-6387	8	13	problems	problem	NOUN
ejpam-6387	8	14	of	of	ADP
ejpam-6387	8	15	integers	integer	NOUN
ejpam-6387	8	16	in	in	ADP
ejpam-6387	8	17	analytic	analytic	ADJ
ejpam-6387	8	18	way	way	NOUN
ejpam-6387	8	19	and	and	CCONJ
ejpam-6387	8	20	some	some	DET
ejpam-6387	8	21	times	time	NOUN
ejpam-6387	8	22	to	to	PART
ejpam-6387	8	23	find	find	VERB
ejpam-6387	8	24	approximate	approximate	ADJ
ejpam-6387	8	25	solutions	solution	NOUN
ejpam-6387	8	26	of	of	ADP
ejpam-6387	8	27	number	number	NOUN
ejpam-6387	8	28	theoritical	theoritical	ADJ
ejpam-6387	8	29	functions	function	NOUN
ejpam-6387	8	30	where	where	SCONJ
ejpam-6387	8	31	exact	exact	ADJ
ejpam-6387	8	32	solutions	solution	NOUN
ejpam-6387	8	33	are	be	AUX
ejpam-6387	8	34	out	out	ADP
ejpam-6387	8	35	of	of	ADP
ejpam-6387	8	36	reach	reach	NOUN
ejpam-6387	8	37	.	.	PUNCT
ejpam-6387	9	1	analytic	analytic	ADJ
ejpam-6387	9	2	number	number	NOUN
ejpam-6387	9	3	theory	theory	NOUN
ejpam-6387	9	4	has	have	VERB
ejpam-6387	9	5	a	a	DET
ejpam-6387	9	6	well	well	ADV
ejpam-6387	9	7	known	know	VERB
ejpam-6387	9	8	results	result	NOUN
ejpam-6387	9	9	on	on	ADP
ejpam-6387	9	10	prime	prime	ADJ
ejpam-6387	9	11	number	number	NOUN
ejpam-6387	9	12	called	call	VERB
ejpam-6387	9	13	prime	prime	ADJ
ejpam-6387	9	14	number	number	NOUN
ejpam-6387	9	15	theorem	theorem	NOUN
ejpam-6387	9	16	which	which	PRON
ejpam-6387	9	17	states	state	VERB
ejpam-6387	9	18	that	that	SCONJ
ejpam-6387	9	19	the	the	DET
ejpam-6387	9	20	number	number	NOUN
ejpam-6387	9	21	of	of	ADP
ejpam-6387	9	22	primes	prime	NOUN
ejpam-6387	9	23	less	less	ADJ
ejpam-6387	9	24	than	than	SCONJ
ejpam-6387	9	25	x	x	X
ejpam-6387	9	26	is	be	AUX
ejpam-6387	9	27	about	about	ADV
ejpam-6387	9	28	x	x	PUNCT
ejpam-6387	9	29	log	log	VERB
ejpam-6387	9	30	x	x	INTJ
ejpam-6387	9	31	.	.	PUNCT
ejpam-6387	10	1	since	since	SCONJ
ejpam-6387	10	2	prime	prime	ADJ
ejpam-6387	10	3	number	number	NOUN
ejpam-6387	10	4	theorem	theorem	NOUN
ejpam-6387	10	5	was	be	AUX
ejpam-6387	10	6	proved	prove	VERB
ejpam-6387	10	7	in	in	ADP
ejpam-6387	10	8	1896	1896	NUM
ejpam-6387	10	9	,	,	PUNCT
ejpam-6387	10	10	independently	independently	ADV
ejpam-6387	10	11	by	by	ADP
ejpam-6387	10	12	hadamard	hadamard	NOUN
ejpam-6387	10	13	and	and	CCONJ
ejpam-6387	10	14	de	de	PROPN
ejpam-6387	10	15	la	la	PROPN
ejpam-6387	10	16	vallee	vallee	PROPN
ejpam-6387	10	17	poussin	poussin	PROPN
ejpam-6387	11	1	[	[	X
ejpam-6387	11	2	1	1	NUM
ejpam-6387	11	3	]	]	PUNCT
ejpam-6387	11	4	,	,	PUNCT
ejpam-6387	11	5	mathematitian	mathematitian	NOUN
ejpam-6387	11	6	have	have	AUX
ejpam-6387	11	7	wondered	wonder	VERB
ejpam-6387	11	8	which	which	DET
ejpam-6387	11	9	condition	condition	NOUN
ejpam-6387	11	10	on	on	ADP
ejpam-6387	11	11	the	the	DET
ejpam-6387	11	12	primes	prime	NOUN
ejpam-6387	11	13	were	be	AUX
ejpam-6387	11	14	really	really	ADV
ejpam-6387	11	15	necessary	necessary	ADJ
ejpam-6387	11	16	to	to	ADP
ejpam-6387	11	17	this	this	DET
ejpam-6387	11	18	kind	kind	NOUN
ejpam-6387	11	19	of	of	ADP
ejpam-6387	11	20	theorems	theorem	NOUN
ejpam-6387	11	21	.	.	PUNCT
ejpam-6387	12	1	during	during	ADP
ejpam-6387	12	2	the	the	DET
ejpam-6387	12	3	1930	1930	NUM
ejpam-6387	12	4	’s	’s	PART
ejpam-6387	12	5	arne	arne	ADJ
ejpam-6387	12	6	beurling	beurling	NOUN
ejpam-6387	12	7	defined	define	VERB
ejpam-6387	12	8	the	the	DET
ejpam-6387	12	9	idea	idea	NOUN
ejpam-6387	12	10	of	of	ADP
ejpam-6387	12	11	generalised	generalise	VERB
ejpam-6387	12	12	prime	prime	ADJ
ejpam-6387	12	13	numbers	number	NOUN
ejpam-6387	12	14	or	or	CCONJ
ejpam-6387	12	15	(	(	PUNCT
ejpam-6387	12	16	beurling	beurle	VERB
ejpam-6387	12	17	primes	prime	NOUN
ejpam-6387	12	18	):	):	PUNCT
ejpam-6387	12	19	any	any	DET
ejpam-6387	12	20	real	real	ADJ
ejpam-6387	12	21	sequence	sequence	NOUN
ejpam-6387	12	22	p	p	NOUN
ejpam-6387	12	23	=	=	PUNCT
ejpam-6387	12	24	{	{	PUNCT
ejpam-6387	12	25	p1	p1	PROPN
ejpam-6387	12	26	,	,	PUNCT
ejpam-6387	12	27	p2	p2	NOUN
ejpam-6387	12	28	,	,	PUNCT
ejpam-6387	12	29	p3	p3	PROPN
ejpam-6387	12	30	,	,	PUNCT
ejpam-6387	12	31	......	......	PUNCT
ejpam-6387	12	32	}	}	PUNCT
ejpam-6387	12	33	satisfying	satisfy	VERB
ejpam-6387	12	34	1	1	NUM
ejpam-6387	12	35	<	<	X
ejpam-6387	12	36	p1	p1	PROPN
ejpam-6387	12	37	≤	≤	PUNCT
ejpam-6387	12	38	p2	p2	PROPN
ejpam-6387	12	39	≤	≤	NUM
ejpam-6387	12	40	p3	p3	PROPN
ejpam-6387	12	41	≤	≤	NOUN
ejpam-6387	12	42	.	.	PUNCT
ejpam-6387	13	1	,	,	PUNCT
ejpam-6387	13	2	.	.	PUNCT
ejpam-6387	13	3	,	,	PUNCT
ejpam-6387	13	4	.	.	PUNCT
ejpam-6387	13	5	,	,	PUNCT
ejpam-6387	13	6	.	.	PUNCT
ejpam-6387	13	7	,	,	PUNCT
ejpam-6387	13	8	.,≤	.,≤	PUNCT
ejpam-6387	14	1	pn	pn	PROPN
ejpam-6387	14	2	≤	≤	PROPN
ejpam-6387	14	3	.......	.......	PUNCT
ejpam-6387	14	4	and	and	CCONJ
ejpam-6387	14	5	pn	pn	VERB
ejpam-6387	14	6	−→	−→	NOUN
ejpam-6387	14	7	∞	∞	PROPN
ejpam-6387	14	8	as	as	ADP
ejpam-6387	14	9	n	n	NUM
ejpam-6387	14	10	−→	−→	NOUN
ejpam-6387	14	11	∞.	∞.	PROPN
ejpam-6387	15	1	so	so	ADV
ejpam-6387	15	2	p	p	NOUN
ejpam-6387	15	3	called	call	VERB
ejpam-6387	15	4	the	the	DET
ejpam-6387	15	5	generalised	generalise	VERB
ejpam-6387	15	6	primes	prime	NOUN
ejpam-6387	15	7	and	and	CCONJ
ejpam-6387	15	8	also	also	ADV
ejpam-6387	15	9	he	he	PRON
ejpam-6387	15	10	∗corresponding	∗corresponde	VERB
ejpam-6387	15	11	author	author	NOUN
ejpam-6387	15	12	.	.	PUNCT
ejpam-6387	16	1	doi	doi	NOUN
ejpam-6387	16	2	:	:	PUNCT
ejpam-6387	16	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6387	https://doi.org/10.29020/nybg.ejpam.v18i4.6387	ADP
ejpam-6387	16	4	email	email	NOUN
ejpam-6387	16	5	addresses	address	NOUN
ejpam-6387	16	6	:	:	PUNCT
ejpam-6387	16	7	zhwan.amen@univsul.edu.iq	zhwan.amen@univsul.edu.iq	PROPN
ejpam-6387	16	8	(	(	PUNCT
ejpam-6387	16	9	z.	z.	PROPN
ejpam-6387	16	10	m.	m.	PROPN
ejpam-6387	16	11	amen	amen	INTJ
ejpam-6387	16	12	)	)	PUNCT
ejpam-6387	16	13	,	,	PUNCT
ejpam-6387	16	14	faez@itnet.uobabylon@edu.iq	faez@itnet.uobabylon@edu.iq	NOUN
ejpam-6387	16	15	(	(	PUNCT
ejpam-6387	16	16	f.	f.	PROPN
ejpam-6387	16	17	a.	a.	PROPN
ejpam-6387	16	18	al	al	PROPN
ejpam-6387	16	19	-	-	PUNCT
ejpam-6387	16	20	maamori	maamori	PROPN
ejpam-6387	16	21	)	)	PUNCT
ejpam-6387	16	22	,	,	PUNCT
ejpam-6387	16	23	mudhafar.hama@univsul.edu.iq	mudhafar.hama@univsul.edu.iq	NOUN
ejpam-6387	16	24	(	(	PUNCT
ejpam-6387	16	25	m.	m.	PROPN
ejpam-6387	16	26	f.	f.	PROPN
ejpam-6387	16	27	hama	hama	PROPN
ejpam-6387	16	28	)	)	PUNCT
ejpam-6387	16	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6387	17	1	1	1	NUM
ejpam-6387	17	2	copyright	copyright	NOUN
ejpam-6387	17	3	:	:	PUNCT
ejpam-6387	17	4	©	©	PROPN
ejpam-6387	17	5	2025	2025	NUM
ejpam-6387	17	6	the	the	DET
ejpam-6387	17	7	author(s	author(s	NOUN
ejpam-6387	17	8	)	)	PUNCT
ejpam-6387	17	9	.	.	PUNCT
ejpam-6387	18	1	(	(	PUNCT
ejpam-6387	18	2	cc	cc	NOUN
ejpam-6387	18	3	by	by	ADP
ejpam-6387	18	4	-	-	PUNCT
ejpam-6387	18	5	nc	nc	PROPN
ejpam-6387	18	6	4.0	4.0	NUM
ejpam-6387	18	7	)	)	PUNCT
ejpam-6387	18	8	z.	z.	PROPN
ejpam-6387	18	9	m.	m.	PROPN
ejpam-6387	18	10	amen	amen	PROPN
ejpam-6387	18	11	,	,	PUNCT
ejpam-6387	18	12	f.	f.	PROPN
ejpam-6387	18	13	a.	a.	PROPN
ejpam-6387	18	14	al	al	PROPN
ejpam-6387	18	15	-	-	PUNCT
ejpam-6387	18	16	maamori	maamori	PROPN
ejpam-6387	18	17	,	,	PUNCT
ejpam-6387	18	18	m.	m.	NOUN
ejpam-6387	18	19	f.	f.	PROPN
ejpam-6387	18	20	hama	hama	PROPN
ejpam-6387	18	21	/	/	SYM
ejpam-6387	18	22	eur	eur	PROPN
ejpam-6387	18	23	.	.	PUNCT
ejpam-6387	19	1	j.	j.	PROPN
ejpam-6387	19	2	pure	pure	PROPN
ejpam-6387	19	3	appl	appl	PROPN
ejpam-6387	19	4	.	.	PROPN
ejpam-6387	19	5	math	math	PROPN
ejpam-6387	19	6	,	,	PUNCT
ejpam-6387	19	7	18	18	NUM
ejpam-6387	19	8	(	(	PUNCT
ejpam-6387	19	9	4	4	NUM
ejpam-6387	19	10	)	)	PUNCT
ejpam-6387	19	11	(	(	PUNCT
ejpam-6387	19	12	2025	2025	NUM
ejpam-6387	19	13	)	)	PUNCT
ejpam-6387	19	14	,	,	PUNCT
ejpam-6387	19	15	6387	6387	NUM
ejpam-6387	19	16	2	2	NUM
ejpam-6387	19	17	of	of	ADP
ejpam-6387	19	18	15	15	NUM
ejpam-6387	19	19	formed	form	VERB
ejpam-6387	19	20	the	the	DET
ejpam-6387	19	21	generalised	generalise	VERB
ejpam-6387	19	22	integers	integer	NOUN
ejpam-6387	19	23	n	n	PRON
ejpam-6387	19	24	(	(	PUNCT
ejpam-6387	19	25	beurling	beurle	VERB
ejpam-6387	19	26	integers	integer	NOUN
ejpam-6387	19	27	)	)	PUNCT
ejpam-6387	19	28	which	which	PRON
ejpam-6387	19	29	is	be	AUX
ejpam-6387	19	30	the	the	DET
ejpam-6387	19	31	product	product	NOUN
ejpam-6387	19	32	of	of	ADP
ejpam-6387	19	33	the	the	DET
ejpam-6387	19	34	form	form	NOUN
ejpam-6387	19	35	n	n	NOUN
ejpam-6387	19	36	=	=	SYM
ejpam-6387	20	1	∏k	∏k	X
ejpam-6387	20	2	i=1	i=1	X
ejpam-6387	21	1	p	p	X
ejpam-6387	22	1	ai	ai	VERB
ejpam-6387	23	1	i	i	PRON
ejpam-6387	23	2	,	,	PUNCT
ejpam-6387	23	3	where	where	SCONJ
ejpam-6387	23	4	k	k	PROPN
ejpam-6387	23	5	∈	∈	PROPN
ejpam-6387	23	6	n	n	ADV
ejpam-6387	23	7	and	and	CCONJ
ejpam-6387	23	8	ai	ai	VERB
ejpam-6387	23	9	∈	∈	PROPN
ejpam-6387	23	10	n	n	ADV
ejpam-6387	23	11	∪	∪	X
ejpam-6387	23	12	{	{	PUNCT
ejpam-6387	23	13	0	0	NUM
ejpam-6387	23	14	}	}	PUNCT
ejpam-6387	23	15	.	.	PUNCT
ejpam-6387	24	1	therefore	therefore	ADV
ejpam-6387	24	2	,	,	PUNCT
ejpam-6387	24	3	the	the	DET
ejpam-6387	24	4	generalised	generalise	VERB
ejpam-6387	24	5	integer	integer	NOUN
ejpam-6387	24	6	or	or	CCONJ
ejpam-6387	24	7	beurling	beurle	VERB
ejpam-6387	24	8	integers	integer	NOUN
ejpam-6387	24	9	can	can	AUX
ejpam-6387	24	10	be	be	AUX
ejpam-6387	24	11	formed	form	VERB
ejpam-6387	24	12	by	by	ADP
ejpam-6387	24	13	the	the	DET
ejpam-6387	24	14	sense	sense	NOUN
ejpam-6387	24	15	of	of	ADP
ejpam-6387	24	16	the	the	DET
ejpam-6387	24	17	fundamental	fundamental	ADJ
ejpam-6387	24	18	theorem	theorem	NOUN
ejpam-6387	24	19	of	of	ADP
ejpam-6387	24	20	arithmetic	arithmetic	NOUN
ejpam-6387	24	21	.	.	PUNCT
ejpam-6387	25	1	in	in	ADP
ejpam-6387	25	2	this	this	DET
ejpam-6387	25	3	sense	sense	NOUN
ejpam-6387	25	4	,	,	PUNCT
ejpam-6387	25	5	beurling	beurling	NOUN
ejpam-6387	25	6	generalises	generalise	VERB
ejpam-6387	25	7	the	the	DET
ejpam-6387	25	8	notion	notion	NOUN
ejpam-6387	25	9	of	of	ADP
ejpam-6387	25	10	prime	prime	ADJ
ejpam-6387	25	11	numbers	number	NOUN
ejpam-6387	25	12	and	and	CCONJ
ejpam-6387	25	13	natural	natural	ADJ
ejpam-6387	25	14	numbers	number	NOUN
ejpam-6387	25	15	.	.	PUNCT
ejpam-6387	26	1	from	from	ADP
ejpam-6387	26	2	the	the	DET
ejpam-6387	26	3	definition	definition	NOUN
ejpam-6387	26	4	realising	realise	VERB
ejpam-6387	26	5	that	that	SCONJ
ejpam-6387	26	6	the	the	DET
ejpam-6387	26	7	generalised	generalise	VERB
ejpam-6387	26	8	prime	prime	NOUN
ejpam-6387	26	9	need	need	AUX
ejpam-6387	26	10	not	not	PART
ejpam-6387	26	11	be	be	AUX
ejpam-6387	26	12	atcual	atcual	ADJ
ejpam-6387	26	13	prime	prime	NOUN
ejpam-6387	26	14	,	,	PUNCT
ejpam-6387	26	15	nor	nor	CCONJ
ejpam-6387	26	16	even	even	ADV
ejpam-6387	26	17	integers	integer	NOUN
ejpam-6387	26	18	.	.	PUNCT
ejpam-6387	27	1	beurling	beurle	VERB
ejpam-6387	27	2	also	also	ADV
ejpam-6387	27	3	defined	define	VERB
ejpam-6387	27	4	πp(x	πp(x	NUM
ejpam-6387	27	5	)	)	PUNCT
ejpam-6387	27	6	to	to	PART
ejpam-6387	27	7	be	be	AUX
ejpam-6387	27	8	the	the	DET
ejpam-6387	27	9	counting	counting	NOUN
ejpam-6387	27	10	function	function	NOUN
ejpam-6387	27	11	of	of	ADP
ejpam-6387	27	12	generalised	generalised	ADJ
ejpam-6387	27	13	prime	prime	NOUN
ejpam-6387	27	14	and	and	CCONJ
ejpam-6387	27	15	np(x	np(x	NUM
ejpam-6387	27	16	)	)	PUNCT
ejpam-6387	27	17	to	to	PART
ejpam-6387	27	18	be	be	AUX
ejpam-6387	27	19	the	the	DET
ejpam-6387	27	20	counting	counting	NOUN
ejpam-6387	27	21	function	function	NOUN
ejpam-6387	27	22	of	of	ADP
ejpam-6387	27	23	generalised	generalise	VERB
ejpam-6387	27	24	integers	integer	NOUN
ejpam-6387	27	25	.	.	PUNCT
ejpam-6387	28	1	beurling	beurle	VERB
ejpam-6387	28	2	also	also	ADV
ejpam-6387	28	3	interested	interested	ADJ
ejpam-6387	28	4	to	to	PART
ejpam-6387	28	5	find	find	VERB
ejpam-6387	28	6	condition	condition	NOUN
ejpam-6387	28	7	on	on	ADP
ejpam-6387	28	8	n	n	NUM
ejpam-6387	28	9	which	which	PRON
ejpam-6387	28	10	let	let	VERB
ejpam-6387	28	11	a	a	DET
ejpam-6387	28	12	prime	prime	ADJ
ejpam-6387	28	13	number	number	NOUN
ejpam-6387	28	14	theorem	theorem	NOUN
ejpam-6387	28	15	holds	hold	NOUN
ejpam-6387	28	16	.	.	PUNCT
ejpam-6387	29	1	in	in	ADP
ejpam-6387	29	2	1937	1937	NUM
ejpam-6387	29	3	,	,	PUNCT
ejpam-6387	29	4	beurling	beurle	VERB
ejpam-6387	29	5	proved	prove	VERB
ejpam-6387	29	6	[	[	X
ejpam-6387	29	7	2	2	X
ejpam-6387	29	8	]	]	PUNCT
ejpam-6387	29	9	that	that	SCONJ
ejpam-6387	29	10	if	if	SCONJ
ejpam-6387	29	11	np(x	np(x	NUM
ejpam-6387	29	12	)	)	PUNCT
ejpam-6387	29	13	=	=	SYM
ejpam-6387	29	14	ax+o	ax+o	PROPN
ejpam-6387	29	15	(	(	PUNCT
ejpam-6387	29	16	x	x	X
ejpam-6387	29	17	(	(	PUNCT
ejpam-6387	29	18	log	log	NOUN
ejpam-6387	29	19	x)γ	x)γ	PUNCT
ejpam-6387	29	20	)	)	PUNCT
ejpam-6387	29	21	for	for	ADP
ejpam-6387	29	22	some	some	PRON
ejpam-6387	29	23	a	a	DET
ejpam-6387	29	24	≥	≥	NOUN
ejpam-6387	29	25	0	0	NUM
ejpam-6387	29	26	and	and	CCONJ
ejpam-6387	29	27	γ	γ	X
ejpam-6387	29	28	greater	great	ADJ
ejpam-6387	29	29	than	than	ADP
ejpam-6387	29	30	3/2	3/2	NUM
ejpam-6387	29	31	,	,	PUNCT
ejpam-6387	29	32	then	then	ADV
ejpam-6387	29	33	πp(x	πp(x	PUNCT
ejpam-6387	29	34	)	)	PUNCT
ejpam-6387	29	35	∼	∼	NOUN
ejpam-6387	29	36	x	x	PUNCT
ejpam-6387	29	37	log	log	NOUN
ejpam-6387	29	38	x	x	INTJ
ejpam-6387	29	39	,	,	PUNCT
ejpam-6387	29	40	this	this	PRON
ejpam-6387	29	41	is	be	AUX
ejpam-6387	29	42	called	call	VERB
ejpam-6387	29	43	beurling	beurle	VERB
ejpam-6387	29	44	prime	prime	ADJ
ejpam-6387	29	45	number	number	NOUN
ejpam-6387	29	46	theorem	theorem	VERB
ejpam-6387	29	47	.	.	PUNCT
ejpam-6387	30	1	lator	lator	PROPN
ejpam-6387	30	2	on	on	ADP
ejpam-6387	30	3	diamond	diamond	NOUN
ejpam-6387	30	4	[	[	X
ejpam-6387	30	5	3	3	NUM
ejpam-6387	30	6	]	]	X
ejpam-6387	30	7	modified	modify	VERB
ejpam-6387	30	8	the	the	DET
ejpam-6387	30	9	definition	definition	NOUN
ejpam-6387	30	10	of	of	ADP
ejpam-6387	30	11	counting	count	VERB
ejpam-6387	30	12	function	function	NOUN
ejpam-6387	30	13	and	and	CCONJ
ejpam-6387	30	14	zeta	zeta	NOUN
ejpam-6387	30	15	function	function	NOUN
ejpam-6387	30	16	using	use	VERB
ejpam-6387	30	17	beurling	beurle	VERB
ejpam-6387	30	18	’s	’s	PART
ejpam-6387	30	19	definitions	definition	NOUN
ejpam-6387	30	20	.	.	PUNCT
ejpam-6387	31	1	since	since	SCONJ
ejpam-6387	31	2	last	last	ADJ
ejpam-6387	31	3	century	century	NOUN
ejpam-6387	31	4	till	till	SCONJ
ejpam-6387	31	5	now	now	ADV
ejpam-6387	31	6	many	many	ADJ
ejpam-6387	31	7	authors	author	NOUN
ejpam-6387	31	8	have	have	AUX
ejpam-6387	31	9	been	be	AUX
ejpam-6387	31	10	dealing	deal	VERB
ejpam-6387	31	11	with	with	ADP
ejpam-6387	31	12	beurling	beurling	NOUN
ejpam-6387	31	13	(	(	PUNCT
ejpam-6387	31	14	generalised	generalised	ADJ
ejpam-6387	31	15	)	)	PUNCT
ejpam-6387	31	16	prime	prime	ADJ
ejpam-6387	31	17	system	system	NOUN
ejpam-6387	31	18	such	such	ADJ
ejpam-6387	31	19	as	as	ADP
ejpam-6387	31	20	bteman	bteman	NOUN
ejpam-6387	31	21	and	and	CCONJ
ejpam-6387	31	22	diamond[4	diamond[4	NOUN
ejpam-6387	31	23	]	]	PUNCT
ejpam-6387	31	24	and	and	CCONJ
ejpam-6387	31	25	so	so	ADV
ejpam-6387	31	26	many	many	ADJ
ejpam-6387	31	27	papers	paper	NOUN
ejpam-6387	31	28	of	of	ADP
ejpam-6387	31	29	diamond[3	diamond[3	PROPN
ejpam-6387	31	30	,	,	PUNCT
ejpam-6387	31	31	5–7	5–7	NOUN
ejpam-6387	31	32	]	]	PUNCT
ejpam-6387	31	33	,	,	PUNCT
ejpam-6387	31	34	maliavin[8	maliavin[8	NOUN
ejpam-6387	31	35	]	]	X
ejpam-6387	31	36	,	,	PUNCT
ejpam-6387	31	37	nyman[9	nyman[9	PROPN
ejpam-6387	31	38	]	]	PUNCT
ejpam-6387	31	39	,	,	PUNCT
ejpam-6387	31	40	hall[10	hall[10	PROPN
ejpam-6387	31	41	]	]	PUNCT
ejpam-6387	31	42	,	,	PUNCT
ejpam-6387	31	43	kahane[11	kahane[11	PROPN
ejpam-6387	31	44	]	]	X
ejpam-6387	31	45	,	,	PUNCT
ejpam-6387	31	46	lagarias[12	lagarias[12	PROPN
ejpam-6387	31	47	]	]	PUNCT
ejpam-6387	31	48	and	and	CCONJ
ejpam-6387	31	49	zhang[13	zhang[13	NOUN
ejpam-6387	31	50	]	]	X
ejpam-6387	31	51	.	.	PUNCT
ejpam-6387	32	1	the	the	DET
ejpam-6387	32	2	major	major	ADJ
ejpam-6387	32	3	reason	reason	NOUN
ejpam-6387	32	4	for	for	ADP
ejpam-6387	32	5	that	that	PRON
ejpam-6387	32	6	is	be	AUX
ejpam-6387	32	7	related	relate	VERB
ejpam-6387	32	8	to	to	ADP
ejpam-6387	32	9	the	the	DET
ejpam-6387	32	10	difficulities	difficulitie	NOUN
ejpam-6387	32	11	of	of	ADP
ejpam-6387	32	12	prove	prove	VERB
ejpam-6387	32	13	or	or	CCONJ
ejpam-6387	32	14	disprove	disprove	VERB
ejpam-6387	32	15	of	of	ADP
ejpam-6387	32	16	riemann	riemann	PROPN
ejpam-6387	32	17	hypothesis	hypothesis	NOUN
ejpam-6387	32	18	as	as	ADP
ejpam-6387	32	19	a	a	DET
ejpam-6387	32	20	special	special	ADJ
ejpam-6387	32	21	case	case	NOUN
ejpam-6387	32	22	of	of	ADP
ejpam-6387	32	23	beurling	beurle	VERB
ejpam-6387	32	24	generalised	generalise	VERB
ejpam-6387	32	25	prime	prime	NOUN
ejpam-6387	32	26	.	.	PUNCT
ejpam-6387	33	1	this	this	DET
ejpam-6387	33	2	article	article	NOUN
ejpam-6387	33	3	introduces	introduce	VERB
ejpam-6387	33	4	some	some	DET
ejpam-6387	33	5	concepts	concept	NOUN
ejpam-6387	33	6	of	of	ADP
ejpam-6387	33	7	generalised	generalised	ADJ
ejpam-6387	33	8	prime	prime	ADJ
ejpam-6387	33	9	counting	counting	NOUN
ejpam-6387	33	10	function	function	NOUN
ejpam-6387	33	11	πp(x	πp(x	NUM
ejpam-6387	33	12	)	)	PUNCT
ejpam-6387	33	13	and	and	CCONJ
ejpam-6387	33	14	concentrates	concentrate	VERB
ejpam-6387	33	15	on	on	ADP
ejpam-6387	33	16	the	the	DET
ejpam-6387	33	17	behavior	behavior	NOUN
ejpam-6387	33	18	of	of	ADP
ejpam-6387	33	19	beurling	beurle	VERB
ejpam-6387	33	20	zeta	zeta	PROPN
ejpam-6387	33	21	function	function	NOUN
ejpam-6387	33	22	ζp(s	ζp(s	NOUN
ejpam-6387	33	23	)	)	PUNCT
ejpam-6387	33	24	in	in	ADP
ejpam-6387	33	25	the	the	DET
ejpam-6387	33	26	strip	strip	NOUN
ejpam-6387	33	27	(	(	PUNCT
ejpam-6387	33	28	0	0	NUM
ejpam-6387	33	29	,	,	PUNCT
ejpam-6387	33	30	1	1	NUM
ejpam-6387	33	31	)	)	PUNCT
ejpam-6387	33	32	and	and	CCONJ
ejpam-6387	33	33	its	its	PRON
ejpam-6387	33	34	effection	effection	NOUN
ejpam-6387	33	35	on	on	ADP
ejpam-6387	33	36	the	the	DET
ejpam-6387	33	37	error	error	NOUN
ejpam-6387	33	38	term	term	NOUN
ejpam-6387	33	39	of	of	ADP
ejpam-6387	33	40	generalised	generalise	VERB
ejpam-6387	33	41	integer	integer	NOUN
ejpam-6387	33	42	counting	counting	NOUN
ejpam-6387	33	43	function	function	NOUN
ejpam-6387	33	44	np(x	np(x	NUM
ejpam-6387	33	45	)	)	PUNCT
ejpam-6387	33	46	.	.	PUNCT
ejpam-6387	34	1	2	2	X
ejpam-6387	34	2	.	.	X
ejpam-6387	34	3	preliminaries	preliminary	NOUN
ejpam-6387	34	4	this	this	DET
ejpam-6387	34	5	section	section	NOUN
ejpam-6387	34	6	gives	give	VERB
ejpam-6387	34	7	some	some	DET
ejpam-6387	34	8	basic	basic	ADJ
ejpam-6387	34	9	concepts	concept	NOUN
ejpam-6387	34	10	and	and	CCONJ
ejpam-6387	34	11	properties	property	NOUN
ejpam-6387	34	12	that	that	PRON
ejpam-6387	34	13	are	be	AUX
ejpam-6387	34	14	needed	need	VERB
ejpam-6387	34	15	for	for	ADP
ejpam-6387	34	16	the	the	DET
ejpam-6387	34	17	aim	aim	NOUN
ejpam-6387	34	18	of	of	ADP
ejpam-6387	34	19	this	this	DET
ejpam-6387	34	20	paper	paper	NOUN
ejpam-6387	34	21	.	.	PUNCT
ejpam-6387	35	1	first	first	ADV
ejpam-6387	35	2	of	of	ADP
ejpam-6387	35	3	all	all	DET
ejpam-6387	35	4	the	the	DET
ejpam-6387	35	5	chebyshev	chebyshev	NOUN
ejpam-6387	35	6	function	function	NOUN
ejpam-6387	35	7	which	which	PRON
ejpam-6387	35	8	is	be	AUX
ejpam-6387	35	9	equivalent	equivalent	ADJ
ejpam-6387	35	10	to	to	ADP
ejpam-6387	35	11	prime	prime	ADJ
ejpam-6387	35	12	counting	counting	NOUN
ejpam-6387	35	13	function	function	NOUN
ejpam-6387	35	14	[	[	X
ejpam-6387	35	15	1	1	X
ejpam-6387	35	16	]	]	PUNCT
ejpam-6387	35	17	is	be	AUX
ejpam-6387	35	18	let	let	VERB
ejpam-6387	35	19	p	p	PRON
ejpam-6387	35	20	be	be	AUX
ejpam-6387	35	21	the	the	DET
ejpam-6387	35	22	set	set	NOUN
ejpam-6387	35	23	of	of	ADP
ejpam-6387	35	24	actual	actual	ADJ
ejpam-6387	35	25	prime	prime	NOUN
ejpam-6387	35	26	,	,	PUNCT
ejpam-6387	35	27	the	the	DET
ejpam-6387	35	28	chebyshev	chebyshev	NOUN
ejpam-6387	35	29	counting	counting	NOUN
ejpam-6387	35	30	function	function	NOUN
ejpam-6387	35	31	for	for	ADP
ejpam-6387	35	32	any	any	DET
ejpam-6387	35	33	positive	positive	ADJ
ejpam-6387	35	34	real	real	NOUN
ejpam-6387	35	35	x	x	VERB
ejpam-6387	35	36	is	be	AUX
ejpam-6387	35	37	defined	define	VERB
ejpam-6387	35	38	to	to	PART
ejpam-6387	35	39	be	be	AUX
ejpam-6387	35	40	ψ(x	ψ(x	NUM
ejpam-6387	35	41	)	)	PUNCT
ejpam-6387	35	42	=	=	PUNCT
ejpam-6387	36	1	∑	∑	PROPN
ejpam-6387	36	2	(	(	PUNCT
ejpam-6387	36	3	pk≤x	pk≤x	PROPN
ejpam-6387	36	4	)	)	PUNCT
ejpam-6387	36	5	log	log	NOUN
ejpam-6387	36	6	p.	p.	NOUN
ejpam-6387	36	7	where	where	SCONJ
ejpam-6387	36	8	k	k	PROPN
ejpam-6387	36	9	∈	∈	PROPN
ejpam-6387	36	10	n	n	PROPN
ejpam-6387	36	11	and	and	CCONJ
ejpam-6387	36	12	p	p	NOUN
ejpam-6387	36	13	∈	∈	PROPN
ejpam-6387	36	14	p	p	NOUN
ejpam-6387	36	15	prime	prime	ADJ
ejpam-6387	36	16	counting	counting	NOUN
ejpam-6387	36	17	function	function	NOUN
ejpam-6387	36	18	[	[	X
ejpam-6387	36	19	1	1	NUM
ejpam-6387	36	20	,	,	PUNCT
ejpam-6387	36	21	14	14	NUM
ejpam-6387	36	22	]	]	PUNCT
ejpam-6387	36	23	is	be	AUX
ejpam-6387	36	24	a	a	DET
ejpam-6387	36	25	number	number	NOUN
ejpam-6387	36	26	prime	prime	NOUN
ejpam-6387	36	27	less	less	ADJ
ejpam-6387	36	28	than	than	ADP
ejpam-6387	36	29	or	or	CCONJ
ejpam-6387	36	30	equal	equal	ADJ
ejpam-6387	36	31	to	to	ADP
ejpam-6387	36	32	x.	x.	NOUN
ejpam-6387	36	33	that	that	PRON
ejpam-6387	36	34	is	be	AUX
ejpam-6387	36	35	π(x	π(x	ADP
ejpam-6387	36	36	)	)	PUNCT
ejpam-6387	37	1	=	=	PUNCT
ejpam-6387	37	2	∑	∑	PROPN
ejpam-6387	37	3	(	(	PUNCT
ejpam-6387	37	4	p≤x	p≤x	PROPN
ejpam-6387	37	5	)	)	PUNCT
ejpam-6387	37	6	1	1	NUM
ejpam-6387	37	7	is	be	AUX
ejpam-6387	37	8	a	a	DET
ejpam-6387	37	9	counting	counting	NOUN
ejpam-6387	37	10	function	function	NOUN
ejpam-6387	37	11	of	of	ADP
ejpam-6387	37	12	primes	prime	NOUN
ejpam-6387	37	13	,	,	PUNCT
ejpam-6387	37	14	for	for	ADP
ejpam-6387	37	15	a	a	DET
ejpam-6387	37	16	large	large	ADJ
ejpam-6387	37	17	value	value	NOUN
ejpam-6387	37	18	x	x	NOUN
ejpam-6387	37	19	,	,	PUNCT
ejpam-6387	37	20	and	and	CCONJ
ejpam-6387	37	21	also	also	ADV
ejpam-6387	37	22	counting	count	VERB
ejpam-6387	37	23	function	function	NOUN
ejpam-6387	37	24	of	of	ADP
ejpam-6387	37	25	integers	integer	NOUN
ejpam-6387	37	26	[	[	X
ejpam-6387	37	27	1	1	NUM
ejpam-6387	37	28	]	]	PUNCT
ejpam-6387	37	29	is	be	AUX
ejpam-6387	37	30	n	n	PRON
ejpam-6387	37	31	(	(	PUNCT
ejpam-6387	37	32	x	x	X
ejpam-6387	37	33	)	)	PUNCT
ejpam-6387	37	34	=	=	SYM
ejpam-6387	37	35	∑	∑	PROPN
ejpam-6387	37	36	(	(	PUNCT
ejpam-6387	37	37	n≤x	n≤x	NOUN
ejpam-6387	37	38	)	)	PUNCT
ejpam-6387	37	39	1	1	NUM
ejpam-6387	37	40	for	for	ADP
ejpam-6387	37	41	a	a	DET
ejpam-6387	37	42	large	large	ADJ
ejpam-6387	37	43	value	value	NOUN
ejpam-6387	37	44	of	of	ADP
ejpam-6387	37	45	x	x	PROPN
ejpam-6387	37	46	,	,	PUNCT
ejpam-6387	37	47	n	n	PROPN
ejpam-6387	37	48	∈	∈	PROPN
ejpam-6387	37	49	n.	n.	NOUN
ejpam-6387	37	50	riemann	riemann	PROPN
ejpam-6387	37	51	zeta	zeta	PROPN
ejpam-6387	37	52	function	function	PROPN
ejpam-6387	37	53	has	have	VERB
ejpam-6387	37	54	an	an	DET
ejpam-6387	37	55	important	important	ADJ
ejpam-6387	37	56	role	role	NOUN
ejpam-6387	37	57	in	in	ADP
ejpam-6387	37	58	analytic	analytic	ADJ
ejpam-6387	37	59	number	number	NOUN
ejpam-6387	37	60	theory	theory	NOUN
ejpam-6387	37	61	and	and	CCONJ
ejpam-6387	37	62	distribution	distribution	NOUN
ejpam-6387	37	63	of	of	ADP
ejpam-6387	37	64	prime	prime	NOUN
ejpam-6387	37	65	which	which	PRON
ejpam-6387	37	66	defined	define	VERB
ejpam-6387	37	67	by	by	ADP
ejpam-6387	37	68	riemann	riemann	PROPN
ejpam-6387	38	1	[	[	X
ejpam-6387	38	2	1	1	NUM
ejpam-6387	38	3	]	]	PUNCT
ejpam-6387	38	4	as	as	ADP
ejpam-6387	38	5	ζ(s	ζ(s	PROPN
ejpam-6387	38	6	)	)	PUNCT
ejpam-6387	38	7	=	=	NOUN
ejpam-6387	38	8	∑∞	∑∞	NOUN
ejpam-6387	38	9	n=1	n=1	PROPN
ejpam-6387	38	10	1	1	NUM
ejpam-6387	38	11	ns	ns	NUM
ejpam-6387	38	12	for	for	ADP
ejpam-6387	38	13	s	s	NOUN
ejpam-6387	38	14	∈	∈	PROPN
ejpam-6387	38	15	c	c	PROPN
ejpam-6387	38	16	and	and	CCONJ
ejpam-6387	38	17	re(s	re(s	ADJ
ejpam-6387	38	18	)	)	PUNCT
ejpam-6387	38	19	≥	≥	NOUN
ejpam-6387	38	20	1	1	NUM
ejpam-6387	38	21	.	.	PUNCT
ejpam-6387	39	1	beurling	beurle	VERB
ejpam-6387	39	2	,	,	PUNCT
ejpam-6387	39	3	as	as	SCONJ
ejpam-6387	39	4	we	we	PRON
ejpam-6387	39	5	mentioned	mention	VERB
ejpam-6387	39	6	before	before	ADV
ejpam-6387	39	7	,	,	PUNCT
ejpam-6387	39	8	generalises	generalise	VERB
ejpam-6387	39	9	the	the	DET
ejpam-6387	39	10	notion	notion	NOUN
ejpam-6387	39	11	of	of	ADP
ejpam-6387	39	12	prime	prime	ADJ
ejpam-6387	39	13	number	number	NOUN
ejpam-6387	39	14	and	and	CCONJ
ejpam-6387	39	15	the	the	DET
ejpam-6387	39	16	natural	natural	ADJ
ejpam-6387	39	17	number	number	NOUN
ejpam-6387	39	18	.	.	PUNCT
ejpam-6387	40	1	beurling	beurling	NOUN
ejpam-6387	40	2	defined	define	VERB
ejpam-6387	40	3	the	the	DET
ejpam-6387	40	4	generalised	generalise	VERB
ejpam-6387	40	5	prime	prime	ADJ
ejpam-6387	40	6	counting	counting	NOUN
ejpam-6387	40	7	function	function	NOUN
ejpam-6387	40	8	[	[	X
ejpam-6387	40	9	15	15	NUM
ejpam-6387	40	10	]	]	PUNCT
ejpam-6387	40	11	as	as	ADP
ejpam-6387	40	12	πp(x	πp(x	NOUN
ejpam-6387	40	13	)	)	PUNCT
ejpam-6387	41	1	=	=	PROPN
ejpam-6387	41	2	∑	∑	PROPN
ejpam-6387	41	3	p≤x	p≤x	PROPN
ejpam-6387	41	4	,	,	PUNCT
ejpam-6387	41	5	p∈p	p∈p	NOUN
ejpam-6387	41	6	1	1	NUM
ejpam-6387	41	7	and	and	CCONJ
ejpam-6387	41	8	generalised	generalise	VERB
ejpam-6387	41	9	integer	integer	NOUN
ejpam-6387	41	10	counting	count	VERB
ejpam-6387	41	11	function	function	NOUN
ejpam-6387	41	12	np(x	np(x	PRON
ejpam-6387	41	13	)	)	PUNCT
ejpam-6387	41	14	=	=	SYM
ejpam-6387	41	15	∑	∑	PUNCT
ejpam-6387	41	16	n≤x	n≤x	PROPN
ejpam-6387	41	17	,	,	PUNCT
ejpam-6387	41	18	n∈n	n∈n	NOUN
ejpam-6387	41	19	1	1	NUM
ejpam-6387	41	20	.	.	PUNCT
ejpam-6387	42	1	beurling	beurle	VERB
ejpam-6387	42	2	also	also	ADV
ejpam-6387	42	3	generalised	generalise	VERB
ejpam-6387	42	4	the	the	DET
ejpam-6387	42	5	zeta	zeta	NOUN
ejpam-6387	42	6	function	function	NOUN
ejpam-6387	42	7	[	[	X
ejpam-6387	42	8	15	15	NUM
ejpam-6387	42	9	]	]	PUNCT
ejpam-6387	42	10	as	as	ADP
ejpam-6387	42	11	ζp(s	ζp(s	NOUN
ejpam-6387	42	12	)	)	PUNCT
ejpam-6387	42	13	=	=	SYM
ejpam-6387	43	1	∑	∑	PUNCT
ejpam-6387	43	2	n∈np	n∈np	NOUN
ejpam-6387	43	3	n−s	n−	VERB
ejpam-6387	43	4	when	when	SCONJ
ejpam-6387	43	5	re(s	re(s	ADJ
ejpam-6387	43	6	)	)	PUNCT
ejpam-6387	43	7	>	>	X
ejpam-6387	43	8	1	1	NUM
ejpam-6387	43	9	,	,	PUNCT
ejpam-6387	43	10	s	s	VERB
ejpam-6387	43	11	∈	∈	PROPN
ejpam-6387	43	12	c	c	NOUN
ejpam-6387	43	13	which	which	PRON
ejpam-6387	43	14	is	be	AUX
ejpam-6387	43	15	z.	z.	PROPN
ejpam-6387	43	16	m.	m.	PROPN
ejpam-6387	43	17	amen	amen	PROPN
ejpam-6387	43	18	,	,	PUNCT
ejpam-6387	43	19	f.	f.	PROPN
ejpam-6387	43	20	a.	a.	PROPN
ejpam-6387	43	21	al	al	PROPN
ejpam-6387	43	22	-	-	PUNCT
ejpam-6387	43	23	maamori	maamori	PROPN
ejpam-6387	43	24	,	,	PUNCT
ejpam-6387	43	25	m.	m.	NOUN
ejpam-6387	43	26	f.	f.	PROPN
ejpam-6387	43	27	hama	hama	PROPN
ejpam-6387	43	28	/	/	SYM
ejpam-6387	43	29	eur	eur	PROPN
ejpam-6387	43	30	.	.	PUNCT
ejpam-6387	44	1	j.	j.	PROPN
ejpam-6387	44	2	pure	pure	PROPN
ejpam-6387	44	3	appl	appl	PROPN
ejpam-6387	44	4	.	.	PROPN
ejpam-6387	44	5	math	math	PROPN
ejpam-6387	44	6	,	,	PUNCT
ejpam-6387	44	7	18	18	NUM
ejpam-6387	44	8	(	(	PUNCT
ejpam-6387	44	9	4	4	NUM
ejpam-6387	44	10	)	)	PUNCT
ejpam-6387	44	11	(	(	PUNCT
ejpam-6387	44	12	2025	2025	NUM
ejpam-6387	44	13	)	)	PUNCT
ejpam-6387	44	14	,	,	PUNCT
ejpam-6387	44	15	6387	6387	NUM
ejpam-6387	44	16	3	3	NUM
ejpam-6387	44	17	of	of	ADP
ejpam-6387	44	18	15	15	NUM
ejpam-6387	44	19	called	call	VERB
ejpam-6387	44	20	beurling	beurle	VERB
ejpam-6387	44	21	zeta	zeta	NOUN
ejpam-6387	44	22	function	function	NOUN
ejpam-6387	44	23	and	and	CCONJ
ejpam-6387	44	24	also	also	ADV
ejpam-6387	44	25	has	have	VERB
ejpam-6387	44	26	several	several	ADJ
ejpam-6387	44	27	definitions	definition	NOUN
ejpam-6387	44	28	related	relate	VERB
ejpam-6387	44	29	to	to	ADP
ejpam-6387	44	30	its	its	PRON
ejpam-6387	44	31	relation	relation	NOUN
ejpam-6387	44	32	with	with	ADP
ejpam-6387	44	33	the	the	DET
ejpam-6387	44	34	counting	counting	NOUN
ejpam-6387	44	35	function	function	NOUN
ejpam-6387	44	36	of	of	ADP
ejpam-6387	44	37	primes	prime	NOUN
ejpam-6387	44	38	and	and	CCONJ
ejpam-6387	44	39	integers	integer	NOUN
ejpam-6387	44	40	:	:	PUNCT
ejpam-6387	44	41	(	(	PUNCT
ejpam-6387	44	42	i	i	NOUN
ejpam-6387	44	43	)	)	PUNCT
ejpam-6387	44	44	ζp(s	ζp(s	NUM
ejpam-6387	44	45	)	)	PUNCT
ejpam-6387	44	46	=	=	PRON
ejpam-6387	44	47	∫∞	∫∞	NOUN
ejpam-6387	44	48	1	1	NUM
ejpam-6387	44	49	x−sdn	x−sdn	NOUN
ejpam-6387	44	50	(	(	PUNCT
ejpam-6387	44	51	x	x	NOUN
ejpam-6387	44	52	)	)	PUNCT
ejpam-6387	44	53	,	,	PUNCT
ejpam-6387	44	54	(	(	PUNCT
ejpam-6387	44	55	ii	ii	NOUN
ejpam-6387	44	56	)	)	PUNCT
ejpam-6387	44	57	−ζp(s	−ζp(s	NUM
ejpam-6387	44	58	)	)	PUNCT
ejpam-6387	44	59	ζp(s	ζp(s	NUM
ejpam-6387	44	60	)	)	PUNCT
ejpam-6387	44	61	=	=	PRON
ejpam-6387	44	62	∫∞	∫∞	NOUN
ejpam-6387	44	63	1	1	NUM
ejpam-6387	44	64	x−sdψ(x	x−sdψ(x	NUM
ejpam-6387	44	65	)	)	PUNCT
ejpam-6387	44	66	,	,	PUNCT
ejpam-6387	44	67	(	(	PUNCT
ejpam-6387	44	68	iii	iii	NOUN
ejpam-6387	44	69	)	)	PUNCT
ejpam-6387	44	70	ζp(s	ζp(s	NOUN
ejpam-6387	44	71	)	)	PUNCT
ejpam-6387	45	1	=	=	SYM
ejpam-6387	45	2	exp	exp	NOUN
ejpam-6387	45	3	∫∞	∫∞	NOUN
ejpam-6387	45	4	1	1	NUM
ejpam-6387	45	5	x−sdπp(x	x−sdπp(x	PROPN
ejpam-6387	45	6	)	)	PUNCT
ejpam-6387	45	7	the	the	DET
ejpam-6387	45	8	above	above	ADJ
ejpam-6387	45	9	definitions	definition	NOUN
ejpam-6387	45	10	shows	show	VERB
ejpam-6387	45	11	the	the	DET
ejpam-6387	45	12	link	link	NOUN
ejpam-6387	45	13	between	between	ADP
ejpam-6387	45	14	ζp(s	ζp(s	NOUN
ejpam-6387	45	15	)	)	PUNCT
ejpam-6387	45	16	,	,	PUNCT
ejpam-6387	45	17	πp(x	πp(x	X
ejpam-6387	45	18	)	)	PUNCT
ejpam-6387	45	19	or	or	CCONJ
ejpam-6387	45	20	ψp(x	ψp(x	NUM
ejpam-6387	45	21	)	)	PUNCT
ejpam-6387	45	22	,	,	PUNCT
ejpam-6387	45	23	and	and	CCONJ
ejpam-6387	45	24	np(x	np(x	NUM
ejpam-6387	45	25	)	)	PUNCT
ejpam-6387	45	26	which	which	PRON
ejpam-6387	45	27	indicated	indicate	VERB
ejpam-6387	45	28	that	that	SCONJ
ejpam-6387	45	29	if	if	SCONJ
ejpam-6387	45	30	we	we	PRON
ejpam-6387	45	31	know	know	VERB
ejpam-6387	45	32	the	the	DET
ejpam-6387	45	33	behavior	behavior	NOUN
ejpam-6387	45	34	of	of	ADP
ejpam-6387	45	35	each	each	DET
ejpam-6387	45	36	one	one	NUM
ejpam-6387	45	37	,	,	PUNCT
ejpam-6387	45	38	say	say	VERB
ejpam-6387	45	39	ψp(x	ψp(x	PUNCT
ejpam-6387	45	40	)	)	PUNCT
ejpam-6387	45	41	,	,	PUNCT
ejpam-6387	45	42	then	then	ADV
ejpam-6387	45	43	we	we	PRON
ejpam-6387	45	44	could	could	AUX
ejpam-6387	45	45	know	know	VERB
ejpam-6387	45	46	the	the	DET
ejpam-6387	45	47	behavior	behavior	NOUN
ejpam-6387	45	48	of	of	ADP
ejpam-6387	45	49	ζp(s	ζp(s	NOUN
ejpam-6387	45	50	)	)	PUNCT
ejpam-6387	45	51	and	and	CCONJ
ejpam-6387	45	52	np(x	np(x	NUM
ejpam-6387	45	53	)	)	PUNCT
ejpam-6387	45	54	.	.	PUNCT
ejpam-6387	46	1	the	the	DET
ejpam-6387	46	2	following	follow	VERB
ejpam-6387	46	3	basic	basic	ADJ
ejpam-6387	46	4	definitions	definition	NOUN
ejpam-6387	46	5	are	be	AUX
ejpam-6387	46	6	introduced	introduce	VERB
ejpam-6387	46	7	since	since	SCONJ
ejpam-6387	46	8	this	this	DET
ejpam-6387	46	9	work	work	NOUN
ejpam-6387	46	10	is	be	AUX
ejpam-6387	46	11	focusing	focus	VERB
ejpam-6387	46	12	on	on	ADP
ejpam-6387	46	13	upper	upper	ADJ
ejpam-6387	46	14	bound	bind	VERB
ejpam-6387	46	15	of	of	ADP
ejpam-6387	46	16	generalised	generalise	VERB
ejpam-6387	46	17	counting	counting	NOUN
ejpam-6387	46	18	function	function	NOUN
ejpam-6387	46	19	np(x	np(x	NOUN
ejpam-6387	46	20	)	)	PUNCT
ejpam-6387	46	21	.	.	PUNCT
ejpam-6387	47	1	definition	definition	NOUN
ejpam-6387	47	2	1	1	NUM
ejpam-6387	47	3	.	.	PUNCT
ejpam-6387	48	1	big	big	ADJ
ejpam-6387	48	2	-	-	PUNCT
ejpam-6387	48	3	o	o	NOUN
ejpam-6387	48	4	-	-	PUNCT
ejpam-6387	48	5	notation[1	notation[1	PROPN
ejpam-6387	48	6	]	]	PUNCT
ejpam-6387	48	7	.	.	PUNCT
ejpam-6387	49	1	let	let	VERB
ejpam-6387	49	2	g(x	g(x	NOUN
ejpam-6387	49	3	)	)	PUNCT
ejpam-6387	49	4	≥	≥	NOUN
ejpam-6387	49	5	0	0	NUM
ejpam-6387	49	6	for	for	ADP
ejpam-6387	49	7	all	all	DET
ejpam-6387	49	8	x	x	SYM
ejpam-6387	49	9	≥	≥	NUM
ejpam-6387	49	10	a.	a.	NOUN
ejpam-6387	49	11	we	we	PRON
ejpam-6387	49	12	write	write	VERB
ejpam-6387	49	13	f(x	f(x	PROPN
ejpam-6387	49	14	)	)	PUNCT
ejpam-6387	50	1	=	=	PUNCT
ejpam-6387	50	2	o(g(x	o(g(x	NOUN
ejpam-6387	50	3	)	)	PUNCT
ejpam-6387	50	4	)	)	PUNCT
ejpam-6387	50	5	or	or	CCONJ
ejpam-6387	50	6	f(x	f(x	PROPN
ejpam-6387	50	7	)	)	PUNCT
ejpam-6387	50	8	�	�	PROPN
ejpam-6387	50	9	g(x	g(x	NOUN
ejpam-6387	50	10	)	)	PUNCT
ejpam-6387	50	11	to	to	PART
ejpam-6387	50	12	mean	mean	VERB
ejpam-6387	50	13	that	that	SCONJ
ejpam-6387	50	14	the	the	DET
ejpam-6387	50	15	quotient	quotient	NOUN
ejpam-6387	50	16	∣∣∣f(x)g(x	∣∣∣f(x)g(x	NOUN
ejpam-6387	50	17	)	)	PUNCT
ejpam-6387	50	18	∣∣∣	∣∣∣	NOUN
ejpam-6387	50	19	is	be	AUX
ejpam-6387	50	20	bounded	bound	VERB
ejpam-6387	50	21	for	for	ADP
ejpam-6387	50	22	x	x	X
ejpam-6387	50	23	≥	≥	X
ejpam-6387	50	24	a	a	NOUN
ejpam-6387	50	25	;	;	PUNCT
ejpam-6387	50	26	that	that	ADV
ejpam-6387	50	27	is	is	ADV
ejpam-6387	50	28	,	,	PUNCT
ejpam-6387	50	29	there	there	PRON
ejpam-6387	50	30	exists	exist	VERB
ejpam-6387	50	31	a	a	DET
ejpam-6387	50	32	constant	constant	ADJ
ejpam-6387	50	33	m	m	NOUN
ejpam-6387	50	34	>	>	X
ejpam-6387	50	35	0	0	NUM
ejpam-6387	51	1	such	such	ADJ
ejpam-6387	51	2	that	that	SCONJ
ejpam-6387	51	3	|f(x)|	|f(x)|	NOUN
ejpam-6387	51	4	≤	≤	NUM
ejpam-6387	51	5	mg(x	mg(x	PUNCT
ejpam-6387	51	6	)	)	PUNCT
ejpam-6387	51	7	for	for	ADP
ejpam-6387	51	8	all	all	DET
ejpam-6387	51	9	x	x	SYM
ejpam-6387	51	10	≥	≥	NUM
ejpam-6387	51	11	a.	a.	NOUN
ejpam-6387	51	12	an	an	DET
ejpam-6387	51	13	equation	equation	NOUN
ejpam-6387	51	14	of	of	ADP
ejpam-6387	51	15	the	the	DET
ejpam-6387	51	16	form	form	NOUN
ejpam-6387	51	17	f(x	f(x	PROPN
ejpam-6387	51	18	)	)	PUNCT
ejpam-6387	52	1	=	=	PUNCT
ejpam-6387	52	2	o(g(x	o(g(x	NOUN
ejpam-6387	52	3	)	)	PUNCT
ejpam-6387	52	4	)	)	PUNCT
ejpam-6387	53	1	+	+	CCONJ
ejpam-6387	53	2	h(x	h(x	PROPN
ejpam-6387	53	3	)	)	PUNCT
ejpam-6387	53	4	means	mean	VERB
ejpam-6387	53	5	that	that	SCONJ
ejpam-6387	53	6	f(x)−	f(x)−	PROPN
ejpam-6387	53	7	h(x	h(x	PROPN
ejpam-6387	53	8	)	)	PUNCT
ejpam-6387	54	1	=	=	PUNCT
ejpam-6387	54	2	o(g(x	o(g(x	NOUN
ejpam-6387	54	3	)	)	PUNCT
ejpam-6387	54	4	)	)	PUNCT
ejpam-6387	54	5	.	.	PUNCT
ejpam-6387	55	1	definition	definition	NOUN
ejpam-6387	55	2	2	2	NUM
ejpam-6387	55	3	.	.	PUNCT
ejpam-6387	56	1	asymptotic	asymptotic	ADJ
ejpam-6387	56	2	notation	notation	NOUN
ejpam-6387	56	3	[	[	X
ejpam-6387	56	4	1]let	1]let	ADJ
ejpam-6387	56	5	g(x	g(x	NOUN
ejpam-6387	56	6	)	)	PUNCT
ejpam-6387	56	7	>	>	X
ejpam-6387	56	8	0	0	PUNCT
ejpam-6387	57	1	for	for	ADP
ejpam-6387	57	2	all	all	DET
ejpam-6387	57	3	x	x	PRON
ejpam-6387	57	4	≥	≥	NUM
ejpam-6387	57	5	a.	a.	NOUN
ejpam-6387	57	6	if	if	SCONJ
ejpam-6387	57	7	lim	lim	PROPN
ejpam-6387	57	8	x−→∞	x−→∞	PROPN
ejpam-6387	57	9	f(x	f(x	PROPN
ejpam-6387	57	10	)	)	PUNCT
ejpam-6387	57	11	g(x	g(x	NOUN
ejpam-6387	57	12	)	)	PUNCT
ejpam-6387	57	13	=	=	SYM
ejpam-6387	57	14	1	1	NUM
ejpam-6387	57	15	we	we	PRON
ejpam-6387	57	16	say	say	VERB
ejpam-6387	57	17	that	that	SCONJ
ejpam-6387	57	18	f(x	f(x	PROPN
ejpam-6387	57	19	)	)	PUNCT
ejpam-6387	57	20	is	be	AUX
ejpam-6387	57	21	asymptotic	asymptotic	ADJ
ejpam-6387	57	22	to	to	ADP
ejpam-6387	57	23	g(x	g(x	NOUN
ejpam-6387	57	24	)	)	PUNCT
ejpam-6387	57	25	as	as	ADP
ejpam-6387	57	26	(	(	PUNCT
ejpam-6387	57	27	x→	x→	NOUN
ejpam-6387	57	28	∞	∞	NUM
ejpam-6387	57	29	)	)	PUNCT
ejpam-6387	57	30	,	,	PUNCT
ejpam-6387	57	31	and	and	CCONJ
ejpam-6387	57	32	we	we	PRON
ejpam-6387	57	33	write	write	VERB
ejpam-6387	57	34	f(x	f(x	PROPN
ejpam-6387	57	35	)	)	PUNCT
ejpam-6387	57	36	∼	∼	NOUN
ejpam-6387	57	37	g(x	g(x	NOUN
ejpam-6387	57	38	)	)	PUNCT
ejpam-6387	57	39	as	as	ADP
ejpam-6387	57	40	(	(	PUNCT
ejpam-6387	57	41	x→	x→	NOUN
ejpam-6387	57	42	∞	∞	NUM
ejpam-6387	57	43	)	)	PUNCT
ejpam-6387	57	44	.	.	PUNCT
ejpam-6387	58	1	definition	definition	NOUN
ejpam-6387	58	2	3	3	NUM
ejpam-6387	58	3	.	.	PUNCT
ejpam-6387	59	1	big	big	ADJ
ejpam-6387	59	2	-	-	PUNCT
ejpam-6387	59	3	omega	omega	NOUN
ejpam-6387	59	4	notation	notation	NOUN
ejpam-6387	59	5	[	[	X
ejpam-6387	59	6	1	1	NUM
ejpam-6387	59	7	]	]	PUNCT
ejpam-6387	59	8	let	let	VERB
ejpam-6387	59	9	g(x	g(x	NOUN
ejpam-6387	59	10	)	)	PUNCT
ejpam-6387	59	11	≥	≥	NOUN
ejpam-6387	59	12	0	0	NUM
ejpam-6387	59	13	for	for	ADP
ejpam-6387	59	14	all	all	DET
ejpam-6387	59	15	x	x	SYM
ejpam-6387	59	16	≥	≥	NUM
ejpam-6387	59	17	a.	a.	NOUN
ejpam-6387	59	18	we	we	PRON
ejpam-6387	59	19	write	write	VERB
ejpam-6387	59	20	f(x	f(x	PROPN
ejpam-6387	59	21	)	)	PUNCT
ejpam-6387	59	22	=	=	SYM
ejpam-6387	59	23	ω(g(x	ω(g(x	NUM
ejpam-6387	59	24	)	)	PUNCT
ejpam-6387	59	25	)	)	PUNCT
ejpam-6387	59	26	or	or	CCONJ
ejpam-6387	59	27	f(x	f(x	PROPN
ejpam-6387	59	28	)	)	PUNCT
ejpam-6387	59	29	�	�	PROPN
ejpam-6387	59	30	g(x	g(x	NOUN
ejpam-6387	59	31	)	)	PUNCT
ejpam-6387	59	32	to	to	PART
ejpam-6387	59	33	mean	mean	VERB
ejpam-6387	59	34	that	that	SCONJ
ejpam-6387	59	35	the	the	DET
ejpam-6387	59	36	quotient	quotient	NOUN
ejpam-6387	59	37	∣∣∣f(x)g(x	∣∣∣f(x)g(x	NOUN
ejpam-6387	59	38	)	)	PUNCT
ejpam-6387	59	39	∣∣∣	∣∣∣	NOUN
ejpam-6387	59	40	is	be	AUX
ejpam-6387	59	41	bounded	bound	VERB
ejpam-6387	59	42	for	for	ADP
ejpam-6387	59	43	x	x	X
ejpam-6387	59	44	≥	≥	X
ejpam-6387	59	45	a	a	NOUN
ejpam-6387	59	46	;	;	PUNCT
ejpam-6387	59	47	that	that	ADV
ejpam-6387	59	48	is	is	ADV
ejpam-6387	59	49	,	,	PUNCT
ejpam-6387	59	50	there	there	PRON
ejpam-6387	59	51	exists	exist	VERB
ejpam-6387	59	52	a	a	DET
ejpam-6387	59	53	constant	constant	ADJ
ejpam-6387	59	54	m	m	NOUN
ejpam-6387	59	55	>	>	X
ejpam-6387	59	56	0	0	NUM
ejpam-6387	60	1	such	such	ADJ
ejpam-6387	60	2	that	that	SCONJ
ejpam-6387	60	3	|f(x)|	|f(x)|	NOUN
ejpam-6387	60	4	≥mg(x	≥mg(x	NOUN
ejpam-6387	60	5	)	)	PUNCT
ejpam-6387	60	6	for	for	ADP
ejpam-6387	60	7	all	all	DET
ejpam-6387	60	8	x	x	SYM
ejpam-6387	60	9	≥	≥	NUM
ejpam-6387	60	10	a.	a.	NOUN
ejpam-6387	60	11	lemma	lemma	PROPN
ejpam-6387	60	12	1	1	NUM
ejpam-6387	60	13	.	.	PUNCT
ejpam-6387	61	1	[	[	X
ejpam-6387	61	2	16	16	NUM
ejpam-6387	61	3	]	]	PUNCT
ejpam-6387	61	4	suppose	suppose	VERB
ejpam-6387	61	5	ψp(x	ψp(x	PUNCT
ejpam-6387	61	6	)	)	PUNCT
ejpam-6387	61	7	=	=	SYM
ejpam-6387	62	1	x	x	PUNCT
ejpam-6387	62	2	+	+	PUNCT
ejpam-6387	62	3	o(xα	o(xα	NUM
ejpam-6387	62	4	)	)	PUNCT
ejpam-6387	62	5	for	for	ADP
ejpam-6387	62	6	some	some	DET
ejpam-6387	62	7	α	α	NOUN
ejpam-6387	62	8	∈	∈	PROPN
ejpam-6387	63	1	[	[	X
ejpam-6387	63	2	0	0	NUM
ejpam-6387	63	3	,	,	PUNCT
ejpam-6387	63	4	1	1	NUM
ejpam-6387	63	5	)	)	PUNCT
ejpam-6387	63	6	,	,	PUNCT
ejpam-6387	63	7	then	then	ADV
ejpam-6387	63	8	ζp(s	ζp(s	NUM
ejpam-6387	63	9	)	)	PUNCT
ejpam-6387	63	10	has	have	VERB
ejpam-6387	63	11	analytic	analytic	ADJ
ejpam-6387	63	12	continuation	continuation	NOUN
ejpam-6387	63	13	to	to	ADP
ejpam-6387	63	14	the	the	DET
ejpam-6387	63	15	half	half	ADJ
ejpam-6387	63	16	-	-	PUNCT
ejpam-6387	63	17	plane	plane	NOUN
ejpam-6387	63	18	hα	hα	ADP
ejpam-6387	63	19	=	=	PUNCT
ejpam-6387	63	20	{	{	PUNCT
ejpam-6387	63	21	s	s	X
ejpam-6387	63	22	∈	∈	X
ejpam-6387	63	23	c	c	NOUN
ejpam-6387	63	24	:	:	PUNCT
ejpam-6387	64	1	re(s	re(s	X
ejpam-6387	64	2	)	)	PUNCT
ejpam-6387	64	3	>	>	X
ejpam-6387	65	1	α	α	X
ejpam-6387	65	2	}	}	PUNCT
ejpam-6387	65	3	except	except	SCONJ
ejpam-6387	65	4	for	for	ADP
ejpam-6387	65	5	a	a	DET
ejpam-6387	65	6	simple	simple	ADJ
ejpam-6387	65	7	pole	pole	NOUN
ejpam-6387	65	8	at	at	ADP
ejpam-6387	65	9	s	s	NOUN
ejpam-6387	65	10	=	=	SYM
ejpam-6387	65	11	1	1	NUM
ejpam-6387	65	12	and	and	CCONJ
ejpam-6387	65	13	ζp(s	ζp(s	NUM
ejpam-6387	65	14	)	)	PUNCT
ejpam-6387	65	15	6=	6=	ADP
ejpam-6387	65	16	0	0	NUM
ejpam-6387	65	17	in	in	ADP
ejpam-6387	65	18	this	this	DET
ejpam-6387	65	19	region	region	NOUN
ejpam-6387	65	20	.	.	PUNCT
ejpam-6387	66	1	3	3	X
ejpam-6387	66	2	.	.	X
ejpam-6387	66	3	some	some	DET
ejpam-6387	66	4	known	know	VERB
ejpam-6387	66	5	results	result	NOUN
ejpam-6387	66	6	most	most	ADJ
ejpam-6387	66	7	of	of	ADP
ejpam-6387	66	8	authers	auther	NOUN
ejpam-6387	66	9	on	on	ADP
ejpam-6387	66	10	this	this	DET
ejpam-6387	66	11	subject	subject	NOUN
ejpam-6387	66	12	had	have	AUX
ejpam-6387	66	13	been	be	AUX
ejpam-6387	66	14	working	work	VERB
ejpam-6387	66	15	on	on	ADP
ejpam-6387	66	16	connecting	connect	VERB
ejpam-6387	66	17	the	the	DET
ejpam-6387	66	18	asymptotic	asymptotic	ADJ
ejpam-6387	66	19	behavior	behavior	NOUN
ejpam-6387	66	20	of	of	ADP
ejpam-6387	66	21	the	the	DET
ejpam-6387	66	22	generalised	generalise	VERB
ejpam-6387	66	23	prime	prime	ADJ
ejpam-6387	66	24	systems	system	NOUN
ejpam-6387	66	25	and	and	CCONJ
ejpam-6387	66	26	generalised	generalise	VERB
ejpam-6387	66	27	integer	integer	NOUN
ejpam-6387	66	28	counting	counting	NOUN
ejpam-6387	66	29	function	function	NOUN
ejpam-6387	66	30	involving	involve	VERB
ejpam-6387	66	31	beurling	beurle	VERB
ejpam-6387	66	32	zeta	zeta	NOUN
ejpam-6387	66	33	function	function	NOUN
ejpam-6387	66	34	ζp(s	ζp(s	NOUN
ejpam-6387	66	35	)	)	PUNCT
ejpam-6387	66	36	.	.	PUNCT
ejpam-6387	67	1	we	we	PRON
ejpam-6387	67	2	mean	mean	VERB
ejpam-6387	67	3	by	by	ADP
ejpam-6387	67	4	the	the	DET
ejpam-6387	67	5	word	word	NOUN
ejpam-6387	67	6	{	{	PUNCT
ejpam-6387	67	7	system	system	NOUN
ejpam-6387	67	8	}	}	PUNCT
ejpam-6387	67	9	as	as	SCONJ
ejpam-6387	67	10	follows	follow	VERB
ejpam-6387	67	11	:	:	PUNCT
ejpam-6387	67	12	as	as	ADP
ejpam-6387	67	13	beurling	beurle	VERB
ejpam-6387	67	14	definition	definition	NOUN
ejpam-6387	67	15	satisfies	satisfie	NOUN
ejpam-6387	67	16	for	for	ADP
ejpam-6387	67	17	any	any	DET
ejpam-6387	67	18	real	real	ADJ
ejpam-6387	67	19	sequence	sequence	NOUN
ejpam-6387	67	20	the	the	DET
ejpam-6387	67	21	condition	condition	NOUN
ejpam-6387	67	22	of	of	ADP
ejpam-6387	67	23	beurlings	beurling	NOUN
ejpam-6387	67	24	,	,	PUNCT
ejpam-6387	67	25	this	this	PRON
ejpam-6387	67	26	means	mean	VERB
ejpam-6387	67	27	that	that	SCONJ
ejpam-6387	67	28	there	there	PRON
ejpam-6387	67	29	are	be	VERB
ejpam-6387	67	30	infinitly	infinitly	ADV
ejpam-6387	67	31	many	many	ADJ
ejpam-6387	67	32	real	real	ADJ
ejpam-6387	67	33	sequence	sequence	NOUN
ejpam-6387	67	34	of	of	ADP
ejpam-6387	67	35	beurling	beurling	ADJ
ejpam-6387	67	36	primes	prime	NOUN
ejpam-6387	67	37	which	which	PRON
ejpam-6387	67	38	indicate	indicate	VERB
ejpam-6387	67	39	that	that	SCONJ
ejpam-6387	67	40	there	there	PRON
ejpam-6387	67	41	are	be	VERB
ejpam-6387	67	42	infinitely	infinitely	ADV
ejpam-6387	67	43	many	many	ADJ
ejpam-6387	67	44	explanations	explanation	NOUN
ejpam-6387	67	45	of	of	ADP
ejpam-6387	67	46	the	the	DET
ejpam-6387	67	47	counting	counting	NOUN
ejpam-6387	67	48	functions	function	NOUN
ejpam-6387	67	49	and	and	CCONJ
ejpam-6387	67	50	beurling	beurle	VERB
ejpam-6387	67	51	zeta	zeta	NOUN
ejpam-6387	67	52	function	function	NOUN
ejpam-6387	67	53	related	relate	VERB
ejpam-6387	67	54	to	to	ADP
ejpam-6387	67	55	each	each	DET
ejpam-6387	67	56	other	other	ADJ
ejpam-6387	67	57	.	.	PUNCT
ejpam-6387	68	1	so	so	ADV
ejpam-6387	68	2	,	,	PUNCT
ejpam-6387	68	3	if	if	SCONJ
ejpam-6387	68	4	we	we	PRON
ejpam-6387	68	5	assume	assume	VERB
ejpam-6387	68	6	that	that	SCONJ
ejpam-6387	68	7	b	b	PROPN
ejpam-6387	68	8	is	be	AUX
ejpam-6387	68	9	a	a	DET
ejpam-6387	68	10	set	set	NOUN
ejpam-6387	68	11	of	of	ADP
ejpam-6387	68	12	all	all	DET
ejpam-6387	68	13	arithmetical	arithmetical	ADJ
ejpam-6387	68	14	functions	function	NOUN
ejpam-6387	68	15	.	.	PUNCT
ejpam-6387	69	1	let	let	VERB
ejpam-6387	69	2	s0	s0	PROPN
ejpam-6387	69	3	=	=	PUNCT
ejpam-6387	69	4	{	{	PUNCT
ejpam-6387	69	5	h	h	NOUN
ejpam-6387	69	6	∈	∈	PROPN
ejpam-6387	69	7	b	b	PROPN
ejpam-6387	69	8	:	:	PUNCT
ejpam-6387	69	9	h(1	h(1	PROPN
ejpam-6387	69	10	)	)	PUNCT
ejpam-6387	69	11	=	=	SYM
ejpam-6387	70	1	0	0	NUM
ejpam-6387	70	2	}	}	PUNCT
ejpam-6387	70	3	and	and	CCONJ
ejpam-6387	70	4	s1	s1	PROPN
ejpam-6387	70	5	=	=	PUNCT
ejpam-6387	70	6	{	{	PUNCT
ejpam-6387	70	7	g	g	PROPN
ejpam-6387	70	8	∈	∈	PROPN
ejpam-6387	70	9	b	b	PROPN
ejpam-6387	70	10	:	:	PUNCT
ejpam-6387	70	11	g(1	g(1	NOUN
ejpam-6387	70	12	)	)	PUNCT
ejpam-6387	70	13	=	=	PUNCT
ejpam-6387	71	1	1	1	NUM
ejpam-6387	71	2	}	}	PUNCT
ejpam-6387	71	3	,	,	PUNCT
ejpam-6387	71	4	then	then	ADV
ejpam-6387	71	5	the	the	DET
ejpam-6387	71	6	order	order	NOUN
ejpam-6387	71	7	pair	pair	NOUN
ejpam-6387	71	8	(	(	PUNCT
ejpam-6387	71	9	h	h	NOUN
ejpam-6387	71	10	,	,	PUNCT
ejpam-6387	71	11	g	g	NOUN
ejpam-6387	71	12	)	)	PUNCT
ejpam-6387	71	13	is	be	AUX
ejpam-6387	71	14	called	call	VERB
ejpam-6387	71	15	an	an	DET
ejpam-6387	71	16	outer	outer	ADJ
ejpam-6387	71	17	generalised	generalise	VERB
ejpam-6387	71	18	prime	prime	ADJ
ejpam-6387	71	19	system	system	NOUN
ejpam-6387	71	20	.	.	PUNCT
ejpam-6387	72	1	z.	z.	PROPN
ejpam-6387	72	2	m.	m.	PROPN
ejpam-6387	72	3	amen	amen	INTJ
ejpam-6387	72	4	,	,	PUNCT
ejpam-6387	72	5	f.	f.	PROPN
ejpam-6387	72	6	a.	a.	PROPN
ejpam-6387	72	7	al	al	PROPN
ejpam-6387	72	8	-	-	PUNCT
ejpam-6387	72	9	maamori	maamori	PROPN
ejpam-6387	72	10	,	,	PUNCT
ejpam-6387	72	11	m.	m.	NOUN
ejpam-6387	72	12	f.	f.	PROPN
ejpam-6387	72	13	hama	hama	PROPN
ejpam-6387	72	14	/	/	SYM
ejpam-6387	72	15	eur	eur	PROPN
ejpam-6387	72	16	.	.	PUNCT
ejpam-6387	73	1	j.	j.	PROPN
ejpam-6387	73	2	pure	pure	PROPN
ejpam-6387	73	3	appl	appl	PROPN
ejpam-6387	73	4	.	.	PROPN
ejpam-6387	73	5	math	math	PROPN
ejpam-6387	73	6	,	,	PUNCT
ejpam-6387	73	7	18	18	NUM
ejpam-6387	73	8	(	(	PUNCT
ejpam-6387	73	9	4	4	NUM
ejpam-6387	73	10	)	)	PUNCT
ejpam-6387	73	11	(	(	PUNCT
ejpam-6387	73	12	2025	2025	NUM
ejpam-6387	73	13	)	)	PUNCT
ejpam-6387	73	14	,	,	PUNCT
ejpam-6387	73	15	6387	6387	NUM
ejpam-6387	73	16	4	4	NUM
ejpam-6387	73	17	of	of	ADP
ejpam-6387	73	18	15	15	NUM
ejpam-6387	73	19	inspite	inspite	NOUN
ejpam-6387	73	20	of	of	ADP
ejpam-6387	73	21	the	the	DET
ejpam-6387	73	22	fact	fact	NOUN
ejpam-6387	73	23	that	that	SCONJ
ejpam-6387	73	24	beurling	beurling	NOUN
ejpam-6387	73	25	answered	answer	VERB
ejpam-6387	73	26	so	so	ADV
ejpam-6387	73	27	many	many	ADJ
ejpam-6387	73	28	questions	question	NOUN
ejpam-6387	73	29	about	about	ADP
ejpam-6387	73	30	prime	prime	ADJ
ejpam-6387	73	31	number	number	NOUN
ejpam-6387	73	32	theorem	theorem	VERB
ejpam-6387	73	33	and	and	CCONJ
ejpam-6387	73	34	generalised	generalise	VERB
ejpam-6387	73	35	prime	prime	ADJ
ejpam-6387	73	36	and	and	CCONJ
ejpam-6387	73	37	integer	integer	NOUN
ejpam-6387	73	38	counting	counting	NOUN
ejpam-6387	73	39	functions	function	NOUN
ejpam-6387	73	40	such	such	ADJ
ejpam-6387	73	41	as	as	ADP
ejpam-6387	73	42	beurling	beurle	VERB
ejpam-6387	73	43	prime	prime	ADJ
ejpam-6387	73	44	number	number	NOUN
ejpam-6387	73	45	theorem	theorem	VERB
ejpam-6387	73	46	,	,	PUNCT
ejpam-6387	73	47	there	there	PRON
ejpam-6387	73	48	are	be	VERB
ejpam-6387	73	49	many	many	ADJ
ejpam-6387	73	50	more	more	ADJ
ejpam-6387	73	51	questions	question	NOUN
ejpam-6387	73	52	regarding	regard	VERB
ejpam-6387	73	53	these	these	DET
ejpam-6387	73	54	functions	function	NOUN
ejpam-6387	73	55	.	.	PUNCT
ejpam-6387	74	1	the	the	DET
ejpam-6387	74	2	generalised	generalise	VERB
ejpam-6387	74	3	riemann	riemann	PROPN
ejpam-6387	74	4	zeta	zeta	PROPN
ejpam-6387	74	5	fuction	fuction	NOUN
ejpam-6387	74	6	also	also	ADV
ejpam-6387	74	7	has	have	VERB
ejpam-6387	74	8	an	an	DET
ejpam-6387	74	9	important	important	ADJ
ejpam-6387	74	10	role	role	NOUN
ejpam-6387	74	11	in	in	ADP
ejpam-6387	74	12	the	the	DET
ejpam-6387	74	13	connection	connection	NOUN
ejpam-6387	74	14	of	of	ADP
ejpam-6387	74	15	asymptotic	asymptotic	ADJ
ejpam-6387	74	16	behavior	behavior	NOUN
ejpam-6387	74	17	of	of	ADP
ejpam-6387	74	18	πp(x	πp(x	PROPN
ejpam-6387	74	19	)	)	PUNCT
ejpam-6387	74	20	and	and	CCONJ
ejpam-6387	74	21	np(x	np(x	NUM
ejpam-6387	74	22	)	)	PUNCT
ejpam-6387	74	23	since	since	SCONJ
ejpam-6387	74	24	in	in	ADP
ejpam-6387	74	25	showing	show	VERB
ejpam-6387	74	26	the	the	DET
ejpam-6387	74	27	link	link	NOUN
ejpam-6387	74	28	between	between	ADP
ejpam-6387	74	29	these	these	DET
ejpam-6387	74	30	results	result	VERB
ejpam-6387	74	31	the	the	DET
ejpam-6387	74	32	author	author	NOUN
ejpam-6387	74	33	might	might	AUX
ejpam-6387	74	34	observe	observe	VERB
ejpam-6387	74	35	the	the	DET
ejpam-6387	74	36	beurlinng	beurlinng	ADJ
ejpam-6387	74	37	zeta	zeta	NOUN
ejpam-6387	74	38	function	function	NOUN
ejpam-6387	74	39	ζp(s	ζp(s	NOUN
ejpam-6387	74	40	)	)	PUNCT
ejpam-6387	74	41	is	be	AUX
ejpam-6387	74	42	involved	involve	VERB
ejpam-6387	74	43	which	which	PRON
ejpam-6387	74	44	means	mean	VERB
ejpam-6387	74	45	that	that	SCONJ
ejpam-6387	74	46	the	the	DET
ejpam-6387	74	47	three	three	NUM
ejpam-6387	74	48	functions	function	NOUN
ejpam-6387	74	49	are	be	AUX
ejpam-6387	74	50	related	relate	VERB
ejpam-6387	74	51	to	to	ADP
ejpam-6387	74	52	each	each	DET
ejpam-6387	74	53	others	other	NOUN
ejpam-6387	74	54	in	in	ADP
ejpam-6387	74	55	the	the	DET
ejpam-6387	74	56	sense	sense	NOUN
ejpam-6387	74	57	that	that	SCONJ
ejpam-6387	74	58	an	an	DET
ejpam-6387	74	59	assumption	assumption	NOUN
ejpam-6387	74	60	made	make	VERB
ejpam-6387	74	61	on	on	ADP
ejpam-6387	74	62	πp(x	πp(x	NOUN
ejpam-6387	74	63	)	)	PUNCT
ejpam-6387	74	64	which	which	PRON
ejpam-6387	74	65	is	be	AUX
ejpam-6387	74	66	then	then	ADV
ejpam-6387	74	67	showing	show	VERB
ejpam-6387	74	68	to	to	ADP
ejpam-6387	74	69	the	the	DET
ejpam-6387	74	70	property	property	NOUN
ejpam-6387	74	71	of	of	ADP
ejpam-6387	74	72	ζp(s	ζp(s	NOUN
ejpam-6387	74	73	)	)	PUNCT
ejpam-6387	74	74	(	(	PUNCT
ejpam-6387	74	75	this	this	PRON
ejpam-6387	74	76	is	be	AUX
ejpam-6387	74	77	related	relate	VERB
ejpam-6387	74	78	to	to	ADP
ejpam-6387	74	79	the	the	DET
ejpam-6387	74	80	size	size	NOUN
ejpam-6387	74	81	of	of	ADP
ejpam-6387	74	82	zeta	zeta	PROPN
ejpam-6387	74	83	function	function	NOUN
ejpam-6387	74	84	along	along	ADP
ejpam-6387	74	85	the	the	DET
ejpam-6387	74	86	vertical	vertical	ADJ
ejpam-6387	74	87	line	line	NOUN
ejpam-6387	74	88	)	)	PUNCT
ejpam-6387	74	89	and	and	CCONJ
ejpam-6387	74	90	this	this	PRON
ejpam-6387	74	91	is	be	AUX
ejpam-6387	74	92	then	then	ADV
ejpam-6387	74	93	shown	show	VERB
ejpam-6387	74	94	to	to	PART
ejpam-6387	74	95	imply	imply	VERB
ejpam-6387	74	96	a	a	DET
ejpam-6387	74	97	property	property	NOUN
ejpam-6387	74	98	of	of	ADP
ejpam-6387	74	99	np(x	np(x	NOUN
ejpam-6387	74	100	)	)	PUNCT
ejpam-6387	74	101	and	and	CCONJ
ejpam-6387	74	102	vice	vice	ADV
ejpam-6387	74	103	versa	versa	ADV
ejpam-6387	74	104	.	.	PUNCT
ejpam-6387	75	1	moving	move	VERB
ejpam-6387	75	2	our	our	PRON
ejpam-6387	75	3	attention	attention	NOUN
ejpam-6387	75	4	to	to	PART
ejpam-6387	75	5	list	list	VERB
ejpam-6387	75	6	some	some	DET
ejpam-6387	75	7	previous	previous	ADJ
ejpam-6387	75	8	work	work	NOUN
ejpam-6387	75	9	which	which	PRON
ejpam-6387	75	10	are	be	AUX
ejpam-6387	75	11	relevant	relevant	ADJ
ejpam-6387	75	12	of	of	ADP
ejpam-6387	75	13	this	this	DET
ejpam-6387	75	14	work	work	NOUN
ejpam-6387	75	15	.	.	PUNCT
ejpam-6387	76	1	(	(	PUNCT
ejpam-6387	76	2	i	i	NOUN
ejpam-6387	76	3	)	)	PUNCT
ejpam-6387	76	4	in	in	ADP
ejpam-6387	76	5	1977	1977	NUM
ejpam-6387	76	6	,	,	PUNCT
ejpam-6387	76	7	diamond	diamond	NOUN
ejpam-6387	76	8	[	[	X
ejpam-6387	76	9	7	7	NUM
ejpam-6387	76	10	]	]	PUNCT
ejpam-6387	76	11	showed	show	VERB
ejpam-6387	76	12	the	the	DET
ejpam-6387	76	13	converse	converse	NOUN
ejpam-6387	76	14	of	of	ADP
ejpam-6387	76	15	beurling	beurle	VERB
ejpam-6387	76	16	’s	’s	PART
ejpam-6387	76	17	prime	prime	ADJ
ejpam-6387	76	18	number	number	NOUN
ejpam-6387	76	19	theorem	theorem	VERB
ejpam-6387	76	20	as	as	SCONJ
ejpam-6387	76	21	he	he	PRON
ejpam-6387	76	22	stated	state	VERB
ejpam-6387	76	23	:	:	PUNCT
ejpam-6387	76	24	suppose	suppose	VERB
ejpam-6387	76	25	that	that	SCONJ
ejpam-6387	76	26	∫∞	∫∞	NOUN
ejpam-6387	76	27	2	2	NUM
ejpam-6387	76	28	t−2|πp(t)−	t−2|πp(t)−	PRON
ejpam-6387	76	29	t	t	PROPN
ejpam-6387	76	30	log	log	VERB
ejpam-6387	76	31	t	t	PROPN
ejpam-6387	76	32	|dt	|dt	X
ejpam-6387	76	33	<	<	X
ejpam-6387	76	34	∞	∞	PROPN
ejpam-6387	76	35	,	,	PUNCT
ejpam-6387	76	36	then	then	ADV
ejpam-6387	76	37	there	there	PRON
ejpam-6387	76	38	exist	exist	VERB
ejpam-6387	76	39	a	a	DET
ejpam-6387	76	40	positive	positive	ADJ
ejpam-6387	76	41	constant	constant	ADJ
ejpam-6387	76	42	c	c	NOUN
ejpam-6387	76	43	such	such	ADJ
ejpam-6387	76	44	that	that	DET
ejpam-6387	76	45	np	np	INTJ
ejpam-6387	76	46	(	(	PUNCT
ejpam-6387	76	47	x	x	NOUN
ejpam-6387	76	48	)	)	PUNCT
ejpam-6387	76	49	∼	∼	NOUN
ejpam-6387	76	50	cx	cx	NOUN
ejpam-6387	76	51	as	as	ADP
ejpam-6387	76	52	x→	x→	PROPN
ejpam-6387	76	53	∞	∞	PROPN
ejpam-6387	76	54	(	(	PUNCT
ejpam-6387	76	55	ii	ii	NOUN
ejpam-6387	76	56	)	)	PUNCT
ejpam-6387	76	57	in	in	ADP
ejpam-6387	76	58	1983	1983	NUM
ejpam-6387	76	59	,	,	PUNCT
ejpam-6387	76	60	landau	landau	VERB
ejpam-6387	76	61	[	[	X
ejpam-6387	76	62	17	17	NUM
ejpam-6387	76	63	]	]	PUNCT
ejpam-6387	76	64	proved	prove	VERB
ejpam-6387	76	65	that	that	SCONJ
ejpam-6387	76	66	if	if	SCONJ
ejpam-6387	76	67	np(x	np(x	NUM
ejpam-6387	76	68	)	)	PUNCT
ejpam-6387	76	69	=	=	SYM
ejpam-6387	76	70	ax+o(xθ	ax+o(xθ	PROPN
ejpam-6387	76	71	)	)	PUNCT
ejpam-6387	76	72	,	,	PUNCT
ejpam-6387	76	73	(	(	PUNCT
ejpam-6387	76	74	θ	θ	X
ejpam-6387	76	75	<	<	X
ejpam-6387	76	76	1	1	NUM
ejpam-6387	76	77	)	)	PUNCT
ejpam-6387	76	78	(	(	PUNCT
ejpam-6387	76	79	1	1	X
ejpam-6387	76	80	)	)	PUNCT
ejpam-6387	76	81	then	then	ADV
ejpam-6387	76	82	πp(x	πp(x	PUNCT
ejpam-6387	76	83	)	)	PUNCT
ejpam-6387	76	84	=	=	SYM
ejpam-6387	77	1	li(x	li(x	X
ejpam-6387	77	2	)	)	PUNCT
ejpam-6387	78	1	+	+	X
ejpam-6387	78	2	o(xe−k	o(xe−k	NOUN
ejpam-6387	78	3	√	√	VERB
ejpam-6387	78	4	log	log	NOUN
ejpam-6387	78	5	x	x	NOUN
ejpam-6387	78	6	)	)	PUNCT
ejpam-6387	78	7	for	for	ADP
ejpam-6387	78	8	some	some	PRON
ejpam-6387	78	9	k	k	PROPN
ejpam-6387	78	10	>	>	X
ejpam-6387	78	11	0	0	PROPN
ejpam-6387	78	12	,	,	PUNCT
ejpam-6387	78	13	where	where	SCONJ
ejpam-6387	78	14	li(x	li(x	NOUN
ejpam-6387	78	15	)	)	PUNCT
ejpam-6387	78	16	=	=	SYM
ejpam-6387	79	1	∫	∫	PUNCT
ejpam-6387	79	2	x	x	SYM
ejpam-6387	79	3	2	2	NUM
ejpam-6387	79	4	dt	dt	NOUN
ejpam-6387	79	5	log	log	NOUN
ejpam-6387	79	6	t	t	PROPN
ejpam-6387	79	7	(	(	PUNCT
ejpam-6387	79	8	iii	iii	NOUN
ejpam-6387	79	9	)	)	PUNCT
ejpam-6387	79	10	in	in	ADP
ejpam-6387	79	11	2006	2006	NUM
ejpam-6387	79	12	,	,	PUNCT
ejpam-6387	79	13	diamond	diamond	NOUN
ejpam-6387	79	14	,	,	PUNCT
ejpam-6387	79	15	montogomery	montogomery	NOUN
ejpam-6387	79	16	and	and	CCONJ
ejpam-6387	79	17	vorhauer	vorhauer	VERB
ejpam-6387	79	18	[	[	X
ejpam-6387	79	19	18	18	NUM
ejpam-6387	79	20	]	]	PUNCT
ejpam-6387	79	21	showed	show	VERB
ejpam-6387	79	22	that	that	SCONJ
ejpam-6387	79	23	landau	landau	NOUN
ejpam-6387	79	24	’s	’s	PART
ejpam-6387	79	25	result	result	NOUN
ejpam-6387	79	26	is	be	AUX
ejpam-6387	79	27	best	good	ADJ
ejpam-6387	79	28	possiblre	possiblre	ADJ
ejpam-6387	79	29	.	.	PUNCT
ejpam-6387	80	1	that	that	PRON
ejpam-6387	80	2	is	be	AUX
ejpam-6387	80	3	they	they	PRON
ejpam-6387	80	4	proved	prove	VERB
ejpam-6387	80	5	that	that	SCONJ
ejpam-6387	80	6	here	here	ADV
ejpam-6387	80	7	is	be	AUX
ejpam-6387	80	8	a	a	DET
ejpam-6387	80	9	discrete	discrete	ADJ
ejpam-6387	80	10	generalised	generalise	VERB
ejpam-6387	80	11	prime	prime	ADJ
ejpam-6387	80	12	system	system	NOUN
ejpam-6387	80	13	for	for	ADP
ejpam-6387	80	14	which	which	DET
ejpam-6387	80	15	equation	equation	NOUN
ejpam-6387	80	16	(	(	PUNCT
ejpam-6387	80	17	1	1	X
ejpam-6387	80	18	)	)	PUNCT
ejpam-6387	80	19	holds	hold	NOUN
ejpam-6387	80	20	but	but	CCONJ
ejpam-6387	80	21	πp(x	πp(x	X
ejpam-6387	80	22	)	)	PUNCT
ejpam-6387	80	23	=	=	SYM
ejpam-6387	81	1	li(x	li(x	NUM
ejpam-6387	81	2	)	)	PUNCT
ejpam-6387	82	1	+	+	CCONJ
ejpam-6387	82	2	ω(xe−q	ω(xe−q	NOUN
ejpam-6387	82	3	√	√	NUM
ejpam-6387	82	4	logx	logx	PROPN
ejpam-6387	82	5	)	)	PUNCT
ejpam-6387	82	6	for	for	ADP
ejpam-6387	82	7	some	some	DET
ejpam-6387	82	8	q	q	NOUN
ejpam-6387	82	9	>	>	X
ejpam-6387	82	10	0	0	PUNCT
ejpam-6387	82	11	(	(	PUNCT
ejpam-6387	82	12	iv	iv	X
ejpam-6387	82	13	)	)	PUNCT
ejpam-6387	82	14	in	in	ADP
ejpam-6387	82	15	1969	1969	NUM
ejpam-6387	82	16	,	,	PUNCT
ejpam-6387	82	17	malliavin	malliavin	X
ejpam-6387	83	1	[	[	X
ejpam-6387	83	2	8	8	NUM
ejpam-6387	83	3	]	]	PUNCT
ejpam-6387	83	4	showed	show	VERB
ejpam-6387	83	5	that	that	SCONJ
ejpam-6387	83	6	for	for	ADP
ejpam-6387	83	7	α	α	DET
ejpam-6387	83	8	∈	∈	PROPN
ejpam-6387	83	9	(	(	PUNCT
ejpam-6387	83	10	0	0	NUM
ejpam-6387	83	11	,	,	PUNCT
ejpam-6387	83	12	1	1	NUM
ejpam-6387	83	13	)	)	PUNCT
ejpam-6387	83	14	and	and	CCONJ
ejpam-6387	83	15	a	a	PRON
ejpam-6387	83	16	,	,	PUNCT
ejpam-6387	83	17	c	c	NOUN
ejpam-6387	83	18	>	>	X
ejpam-6387	83	19	0	0	NUM
ejpam-6387	83	20	np(x	np(x	NUM
ejpam-6387	83	21	)	)	PUNCT
ejpam-6387	83	22	=	=	PUNCT
ejpam-6387	83	23	ax+o(xe−c(log	ax+o(xe−c(log	PROPN
ejpam-6387	83	24	x)β	x)β	NOUN
ejpam-6387	83	25	)	)	PUNCT
ejpam-6387	83	26	implies	imply	VERB
ejpam-6387	83	27	πp(x	πp(x	X
ejpam-6387	83	28	)	)	PUNCT
ejpam-6387	83	29	=	=	SYM
ejpam-6387	84	1	li(x	li(x	X
ejpam-6387	84	2	)	)	PUNCT
ejpam-6387	85	1	+	+	NOUN
ejpam-6387	85	2	o(xe−k(log	o(xe−k(log	NOUN
ejpam-6387	85	3	x)α	x)α	NOUN
ejpam-6387	85	4	)	)	PUNCT
ejpam-6387	85	5	for	for	ADP
ejpam-6387	85	6	some	some	PRON
ejpam-6387	85	7	k	k	PROPN
ejpam-6387	85	8	>	>	X
ejpam-6387	85	9	0	0	NUM
ejpam-6387	86	1	where	where	SCONJ
ejpam-6387	86	2	β	β	X
ejpam-6387	86	3	=	=	SYM
ejpam-6387	86	4	10α	10α	X
ejpam-6387	86	5	(	(	PUNCT
ejpam-6387	86	6	v	v	NOUN
ejpam-6387	86	7	)	)	PUNCT
ejpam-6387	86	8	in	in	ADP
ejpam-6387	86	9	1970	1970	NUM
ejpam-6387	86	10	,	,	PUNCT
ejpam-6387	86	11	diamond	diamond	NOUN
ejpam-6387	86	12	[	[	X
ejpam-6387	86	13	3	3	NUM
ejpam-6387	86	14	]	]	PUNCT
ejpam-6387	86	15	showed	show	VERB
ejpam-6387	86	16	the	the	DET
ejpam-6387	86	17	converse	converse	NOUN
ejpam-6387	86	18	of	of	ADP
ejpam-6387	86	19	malliavin	malliavin	PROPN
ejpam-6387	86	20	’s	’s	PART
ejpam-6387	86	21	result	result	NOUN
ejpam-6387	86	22	,	,	PUNCT
ejpam-6387	86	23	as	as	SCONJ
ejpam-6387	86	24	he	he	PRON
ejpam-6387	86	25	proved	prove	VERB
ejpam-6387	86	26	that	that	SCONJ
ejpam-6387	86	27	if	if	SCONJ
ejpam-6387	86	28	πp(x	πp(x	NUM
ejpam-6387	86	29	)	)	PUNCT
ejpam-6387	87	1	=	=	SYM
ejpam-6387	87	2	li(x	li(x	X
ejpam-6387	87	3	)	)	PUNCT
ejpam-6387	88	1	+	+	NOUN
ejpam-6387	88	2	o(xe−c(logx)α	o(xe−c(logx)α	NOUN
ejpam-6387	88	3	)	)	PUNCT
ejpam-6387	88	4	holds	hold	VERB
ejpam-6387	88	5	for	for	ADP
ejpam-6387	88	6	α	α	PRON
ejpam-6387	88	7	∈	∈	PROPN
ejpam-6387	88	8	(	(	PUNCT
ejpam-6387	88	9	0	0	NUM
ejpam-6387	88	10	,	,	PUNCT
ejpam-6387	88	11	1	1	NUM
ejpam-6387	88	12	)	)	PUNCT
ejpam-6387	88	13	and	and	CCONJ
ejpam-6387	88	14	some	some	PRON
ejpam-6387	88	15	c	c	PROPN
ejpam-6387	88	16	>	>	X
ejpam-6387	88	17	0	0	NUM
ejpam-6387	88	18	,	,	PUNCT
ejpam-6387	88	19	then	then	ADV
ejpam-6387	88	20	np(x	np(x	NUM
ejpam-6387	88	21	)	)	PUNCT
ejpam-6387	88	22	=	=	SYM
ejpam-6387	89	1	ψx+o(xe−b(log	ψx+o(xe−b(log	PROPN
ejpam-6387	89	2	x	x	PUNCT
ejpam-6387	89	3	log	log	NOUN
ejpam-6387	89	4	log	log	NOUN
ejpam-6387	89	5	x)β	x)β	NOUN
ejpam-6387	89	6	)	)	PUNCT
ejpam-6387	89	7	for	for	ADP
ejpam-6387	89	8	some	some	DET
ejpam-6387	89	9	b	b	NOUN
ejpam-6387	89	10	>	>	X
ejpam-6387	89	11	0	0	NUM
ejpam-6387	89	12	where	where	SCONJ
ejpam-6387	89	13	β	β	X
ejpam-6387	89	14	=	=	PUNCT
ejpam-6387	89	15	α	α	PROPN
ejpam-6387	89	16	1+α	1+α	NUM
ejpam-6387	89	17	.	.	PUNCT
ejpam-6387	90	1	z.	z.	PROPN
ejpam-6387	90	2	m.	m.	PROPN
ejpam-6387	90	3	amen	amen	INTJ
ejpam-6387	90	4	,	,	PUNCT
ejpam-6387	90	5	f.	f.	PROPN
ejpam-6387	90	6	a.	a.	PROPN
ejpam-6387	90	7	al	al	PROPN
ejpam-6387	90	8	-	-	PUNCT
ejpam-6387	90	9	maamori	maamori	PROPN
ejpam-6387	90	10	,	,	PUNCT
ejpam-6387	90	11	m.	m.	NOUN
ejpam-6387	90	12	f.	f.	PROPN
ejpam-6387	90	13	hama	hama	PROPN
ejpam-6387	90	14	/	/	SYM
ejpam-6387	90	15	eur	eur	PROPN
ejpam-6387	90	16	.	.	PUNCT
ejpam-6387	91	1	j.	j.	PROPN
ejpam-6387	91	2	pure	pure	PROPN
ejpam-6387	91	3	appl	appl	PROPN
ejpam-6387	91	4	.	.	PROPN
ejpam-6387	91	5	math	math	PROPN
ejpam-6387	91	6	,	,	PUNCT
ejpam-6387	91	7	18	18	NUM
ejpam-6387	91	8	(	(	PUNCT
ejpam-6387	91	9	4	4	NUM
ejpam-6387	91	10	)	)	PUNCT
ejpam-6387	91	11	(	(	PUNCT
ejpam-6387	91	12	2025	2025	NUM
ejpam-6387	91	13	)	)	PUNCT
ejpam-6387	91	14	,	,	PUNCT
ejpam-6387	91	15	6387	6387	NUM
ejpam-6387	91	16	5	5	NUM
ejpam-6387	91	17	of	of	ADP
ejpam-6387	91	18	15	15	NUM
ejpam-6387	91	19	(	(	PUNCT
ejpam-6387	91	20	vi	vi	NOUN
ejpam-6387	91	21	)	)	PUNCT
ejpam-6387	91	22	in	in	ADP
ejpam-6387	91	23	1998	1998	NUM
ejpam-6387	91	24	,	,	PUNCT
ejpam-6387	91	25	balanzario	balanzario	PROPN
ejpam-6387	92	1	[	[	X
ejpam-6387	92	2	19	19	NUM
ejpam-6387	92	3	]	]	PUNCT
ejpam-6387	92	4	showed	show	VERB
ejpam-6387	92	5	by	by	ADP
ejpam-6387	92	6	example	example	NOUN
ejpam-6387	92	7	that	that	SCONJ
ejpam-6387	92	8	there	there	PRON
ejpam-6387	92	9	exists	exist	VERB
ejpam-6387	92	10	a	a	DET
ejpam-6387	92	11	continuous	continuous	ADJ
ejpam-6387	92	12	generalised	generalised	ADJ
ejpam-6387	92	13	prime	prime	ADJ
ejpam-6387	92	14	system	system	NOUN
ejpam-6387	92	15	for	for	ADP
ejpam-6387	92	16	which	which	PRON
ejpam-6387	92	17	πp(x	πp(x	X
ejpam-6387	92	18	)	)	PUNCT
ejpam-6387	92	19	=	=	SYM
ejpam-6387	93	1	li(x	li(x	X
ejpam-6387	93	2	)	)	PUNCT
ejpam-6387	94	1	+	+	ADP
ejpam-6387	94	2	o(xe−(log	o(xe−(log	NOUN
ejpam-6387	94	3	x)α	x)α	NOUN
ejpam-6387	94	4	)	)	PUNCT
ejpam-6387	94	5	and	and	CCONJ
ejpam-6387	94	6	np(x	np(x	NUM
ejpam-6387	94	7	)	)	PUNCT
ejpam-6387	94	8	=	=	SYM
ejpam-6387	94	9	ρx+ω±	ρx+ω±	PROPN
ejpam-6387	94	10	(	(	PUNCT
ejpam-6387	94	11	xe−c(logx)β	xe−c(logx)β	PROPN
ejpam-6387	94	12	)	)	PUNCT
ejpam-6387	94	13	holds	hold	VERB
ejpam-6387	94	14	for	for	ADP
ejpam-6387	94	15	some	some	DET
ejpam-6387	94	16	positive	positive	ADJ
ejpam-6387	94	17	constants	constant	NOUN
ejpam-6387	94	18	ρ	ρ	NOUN
ejpam-6387	94	19	and	and	CCONJ
ejpam-6387	94	20	c	c	NOUN
ejpam-6387	94	21	with	with	ADP
ejpam-6387	94	22	α	α	NOUN
ejpam-6387	94	23	=	=	SYM
ejpam-6387	94	24	β	β	X
ejpam-6387	94	25	=	=	SYM
ejpam-6387	94	26	1	1	NUM
ejpam-6387	94	27	2	2	NUM
ejpam-6387	94	28	.	.	PUNCT
ejpam-6387	95	1	(	(	PUNCT
ejpam-6387	95	2	vii	vii	PROPN
ejpam-6387	95	3	)	)	PUNCT
ejpam-6387	95	4	in	in	ADP
ejpam-6387	95	5	2006	2006	NUM
ejpam-6387	95	6	,	,	PUNCT
ejpam-6387	95	7	hilberdink[16	hilberdink[16	PROPN
ejpam-6387	95	8	]	]	PUNCT
ejpam-6387	95	9	extended	extend	VERB
ejpam-6387	95	10	diamond	diamond	NOUN
ejpam-6387	95	11	’s	’s	PART
ejpam-6387	95	12	result	result	NOUN
ejpam-6387	95	13	in	in	ADP
ejpam-6387	95	14	6	6	NUM
ejpam-6387	95	15	to	to	ADP
ejpam-6387	95	16	the	the	DET
ejpam-6387	95	17	case	case	NOUN
ejpam-6387	95	18	of	of	ADP
ejpam-6387	95	19	α	α	NOUN
ejpam-6387	95	20	=	=	SYM
ejpam-6387	95	21	1	1	NUM
ejpam-6387	95	22	as	as	SCONJ
ejpam-6387	95	23	follows	follow	VERB
ejpam-6387	95	24	:	:	PUNCT
ejpam-6387	95	25	suppose	suppose	VERB
ejpam-6387	95	26	ψp(x	ψp(x	PUNCT
ejpam-6387	95	27	)	)	PUNCT
ejpam-6387	95	28	=	=	SYM
ejpam-6387	96	1	x	x	PUNCT
ejpam-6387	96	2	+	+	PUNCT
ejpam-6387	96	3	o(xα	o(xα	NUM
ejpam-6387	96	4	)	)	PUNCT
ejpam-6387	96	5	for	for	ADP
ejpam-6387	96	6	some	some	DET
ejpam-6387	96	7	α	α	NOUN
ejpam-6387	96	8	∈	∈	PROPN
ejpam-6387	96	9	(	(	PUNCT
ejpam-6387	96	10	0	0	NUM
ejpam-6387	96	11	,	,	PUNCT
ejpam-6387	96	12	1	1	NUM
ejpam-6387	96	13	)	)	PUNCT
ejpam-6387	96	14	then	then	ADV
ejpam-6387	96	15	there	there	PRON
ejpam-6387	96	16	exists	exist	VERB
ejpam-6387	96	17	positive	positive	ADJ
ejpam-6387	96	18	constants	constant	NOUN
ejpam-6387	96	19	ρ	ρ	PROPN
ejpam-6387	96	20	and	and	CCONJ
ejpam-6387	96	21	c	c	NOUN
ejpam-6387	96	22	such	such	ADJ
ejpam-6387	96	23	that	that	PRON
ejpam-6387	96	24	np(x	np(x	PRON
ejpam-6387	96	25	)	)	PUNCT
ejpam-6387	96	26	=	=	PUNCT
ejpam-6387	97	1	ρx+o(xe−c	ρx+o(xe−c	NOUN
ejpam-6387	97	2	√	√	NUM
ejpam-6387	97	3	log	log	NOUN
ejpam-6387	97	4	x	x	PUNCT
ejpam-6387	97	5	log	log	VERB
ejpam-6387	97	6	log	log	NOUN
ejpam-6387	97	7	x	x	NOUN
ejpam-6387	97	8	)	)	PUNCT
ejpam-6387	97	9	.	.	PUNCT
ejpam-6387	98	1	(	(	PUNCT
ejpam-6387	98	2	viii	viii	NOUN
ejpam-6387	98	3	)	)	PUNCT
ejpam-6387	98	4	in	in	ADP
ejpam-6387	98	5	2014	2014	NUM
ejpam-6387	98	6	,	,	PUNCT
ejpam-6387	98	7	al	al	PROPN
ejpam-6387	98	8	-	-	PUNCT
ejpam-6387	98	9	maamori	maamori	NOUN
ejpam-6387	99	1	[	[	X
ejpam-6387	99	2	15	15	NUM
ejpam-6387	99	3	]	]	PUNCT
ejpam-6387	99	4	showed	show	VERB
ejpam-6387	99	5	by	by	ADP
ejpam-6387	99	6	example	example	NOUN
ejpam-6387	99	7	that	that	SCONJ
ejpam-6387	99	8	there	there	PRON
ejpam-6387	99	9	exists	exist	VERB
ejpam-6387	99	10	a	a	DET
ejpam-6387	99	11	continuous	continuous	ADJ
ejpam-6387	99	12	generalised	generalised	ADJ
ejpam-6387	99	13	prime	prime	ADJ
ejpam-6387	99	14	system	system	NOUN
ejpam-6387	99	15	for	for	ADP
ejpam-6387	99	16	which	which	PRON
ejpam-6387	99	17	πp(x	πp(x	X
ejpam-6387	99	18	)	)	PUNCT
ejpam-6387	99	19	=	=	SYM
ejpam-6387	100	1	li(x	li(x	X
ejpam-6387	100	2	)	)	PUNCT
ejpam-6387	101	1	+	+	ADP
ejpam-6387	101	2	o(xe−(log	o(xe−(log	NOUN
ejpam-6387	101	3	x)α	x)α	NOUN
ejpam-6387	101	4	)	)	PUNCT
ejpam-6387	101	5	and	and	CCONJ
ejpam-6387	101	6	np(x	np(x	NUM
ejpam-6387	101	7	)	)	PUNCT
ejpam-6387	101	8	=	=	SYM
ejpam-6387	101	9	ρx+ω±	ρx+ω±	PROPN
ejpam-6387	101	10	(	(	PUNCT
ejpam-6387	101	11	xe−c(log	xe−c(log	PROPN
ejpam-6387	101	12	x)β	x)β	NUM
ejpam-6387	101	13	)	)	PUNCT
ejpam-6387	101	14	holds	hold	VERB
ejpam-6387	101	15	for	for	ADP
ejpam-6387	101	16	some	some	DET
ejpam-6387	101	17	positive	positive	ADJ
ejpam-6387	101	18	constants	constant	NOUN
ejpam-6387	101	19	ρ	ρ	NOUN
ejpam-6387	101	20	and	and	CCONJ
ejpam-6387	101	21	c	c	NOUN
ejpam-6387	101	22	with	with	ADP
ejpam-6387	101	23	α	α	PROPN
ejpam-6387	101	24	=	=	SYM
ejpam-6387	101	25	β	β	X
ejpam-6387	101	26	.	.	PUNCT
ejpam-6387	102	1	(	(	PUNCT
ejpam-6387	102	2	ix	ix	ADP
ejpam-6387	102	3	)	)	PUNCT
ejpam-6387	102	4	in	in	ADP
ejpam-6387	102	5	2015	2015	NUM
ejpam-6387	102	6	,	,	PUNCT
ejpam-6387	102	7	al	al	PROPN
ejpam-6387	102	8	-	-	PUNCT
ejpam-6387	102	9	maamori	maamori	PROPN
ejpam-6387	102	10	and	and	CCONJ
ejpam-6387	102	11	hilberdink	hilberdink	ADJ
ejpam-6387	103	1	[	[	X
ejpam-6387	103	2	20	20	NUM
ejpam-6387	103	3	]	]	PUNCT
ejpam-6387	103	4	showed	show	VERB
ejpam-6387	103	5	that	that	SCONJ
ejpam-6387	103	6	theorem	theorem	NOUN
ejpam-6387	103	7	1	1	NUM
ejpam-6387	103	8	.	.	PUNCT
ejpam-6387	103	9	suppose	suppose	VERB
ejpam-6387	103	10	that	that	SCONJ
ejpam-6387	103	11	for	for	ADP
ejpam-6387	103	12	some	some	DET
ejpam-6387	103	13	α	α	NOUN
ejpam-6387	103	14	∈	∈	PROPN
ejpam-6387	103	15	(	(	PUNCT
ejpam-6387	103	16	0	0	NUM
ejpam-6387	103	17	,	,	PUNCT
ejpam-6387	103	18	1	1	NUM
ejpam-6387	103	19	)	)	PUNCT
ejpam-6387	103	20	,	,	PUNCT
ejpam-6387	103	21	ζp(s	ζp(s	NUM
ejpam-6387	103	22	)	)	PUNCT
ejpam-6387	103	23	has	have	VERB
ejpam-6387	103	24	an	an	DET
ejpam-6387	103	25	analytic	analytic	ADJ
ejpam-6387	103	26	continuation	continuation	NOUN
ejpam-6387	103	27	to	to	ADP
ejpam-6387	103	28	the	the	DET
ejpam-6387	103	29	half	half	ADJ
ejpam-6387	103	30	plane	plane	NOUN
ejpam-6387	103	31	hα	hα	VERB
ejpam-6387	103	32	except	except	SCONJ
ejpam-6387	103	33	for	for	ADP
ejpam-6387	103	34	a	a	DET
ejpam-6387	103	35	simple	simple	ADJ
ejpam-6387	103	36	pole	pole	NOUN
ejpam-6387	103	37	at	at	ADP
ejpam-6387	103	38	s	s	NOUN
ejpam-6387	103	39	=	=	NOUN
ejpam-6387	103	40	1	1	NUM
ejpam-6387	103	41	with	with	ADP
ejpam-6387	103	42	residue	residue	NOUN
ejpam-6387	103	43	β	β	NOUN
ejpam-6387	103	44	.	.	PUNCT
ejpam-6387	104	1	further	far	ADV
ejpam-6387	104	2	assume	assume	VERB
ejpam-6387	104	3	that	that	SCONJ
ejpam-6387	104	4	for	for	ADP
ejpam-6387	104	5	some	some	DET
ejpam-6387	104	6	c	c	NOUN
ejpam-6387	104	7	<	<	X
ejpam-6387	104	8	1	1	NUM
ejpam-6387	104	9	ζp(σ	ζp(σ	NUM
ejpam-6387	104	10	+	+	CCONJ
ejpam-6387	104	11	it	it	PRON
ejpam-6387	104	12	)	)	PUNCT
ejpam-6387	104	13	=	=	PUNCT
ejpam-6387	105	1	o(tc	o(tc	NUM
ejpam-6387	105	2	)	)	PUNCT
ejpam-6387	105	3	,	,	PUNCT
ejpam-6387	105	4	for	for	ADP
ejpam-6387	105	5	some	some	DET
ejpam-6387	105	6	σ	σ	PROPN
ejpam-6387	105	7	≥	≥	NOUN
ejpam-6387	105	8	1−	1−	NUM
ejpam-6387	105	9	1	1	NUM
ejpam-6387	105	10	f(log	f(log	PROPN
ejpam-6387	105	11	t	t	PROPN
ejpam-6387	105	12	)	)	PUNCT
ejpam-6387	105	13	where	where	SCONJ
ejpam-6387	105	14	f	f	PROPN
ejpam-6387	105	15	is	be	AUX
ejpam-6387	105	16	positive	positive	ADJ
ejpam-6387	105	17	,	,	PUNCT
ejpam-6387	105	18	strictly	strictly	ADV
ejpam-6387	105	19	increasing	increase	VERB
ejpam-6387	105	20	continuous	continuous	ADJ
ejpam-6387	105	21	function	function	NOUN
ejpam-6387	105	22	,	,	PUNCT
ejpam-6387	105	23	tending	tend	VERB
ejpam-6387	105	24	to	to	ADP
ejpam-6387	105	25	infinity	infinity	NOUN
ejpam-6387	105	26	.	.	PUNCT
ejpam-6387	106	1	then	then	ADV
ejpam-6387	106	2	for	for	ADP
ejpam-6387	106	3	γ	γ	X
ejpam-6387	106	4	=	=	SYM
ejpam-6387	106	5	1−	1−	NUM
ejpam-6387	106	6	c	c	NOUN
ejpam-6387	106	7	,	,	PUNCT
ejpam-6387	106	8	np(x	np(x	NUM
ejpam-6387	106	9	)	)	PUNCT
ejpam-6387	106	10	=	=	SYM
ejpam-6387	107	1	βx+o(xe−	βx+o(xe−	PROPN
ejpam-6387	107	2	γ	γ	X
ejpam-6387	107	3	2	2	NUM
ejpam-6387	107	4	h−1(γ−1	h−1(γ−1	PROPN
ejpam-6387	107	5	log	log	NOUN
ejpam-6387	107	6	x	x	NOUN
ejpam-6387	107	7	)	)	PUNCT
ejpam-6387	107	8	)	)	PUNCT
ejpam-6387	107	9	where	where	SCONJ
ejpam-6387	107	10	h(u	h(u	NOUN
ejpam-6387	107	11	)	)	PUNCT
ejpam-6387	107	12	=	=	SYM
ejpam-6387	107	13	uf(u	uf(u	NUM
ejpam-6387	107	14	)	)	PUNCT
ejpam-6387	107	15	.	.	PUNCT
ejpam-6387	108	1	the	the	DET
ejpam-6387	108	2	next	next	ADJ
ejpam-6387	108	3	section	section	NOUN
ejpam-6387	108	4	focus	focus	VERB
ejpam-6387	108	5	on	on	ADP
ejpam-6387	108	6	the	the	DET
ejpam-6387	108	7	theorem	theorem	NOUN
ejpam-6387	108	8	(	(	PUNCT
ejpam-6387	108	9	1	1	NUM
ejpam-6387	108	10	)	)	PUNCT
ejpam-6387	108	11	above	above	ADV
ejpam-6387	108	12	.	.	PUNCT
ejpam-6387	109	1	in	in	ADP
ejpam-6387	109	2	particular	particular	ADJ
ejpam-6387	109	3	,	,	PUNCT
ejpam-6387	109	4	the	the	DET
ejpam-6387	109	5	following	follow	VERB
ejpam-6387	109	6	work	work	NOUN
ejpam-6387	109	7	concentrating	concentrate	VERB
ejpam-6387	109	8	on	on	ADP
ejpam-6387	109	9	the	the	DET
ejpam-6387	109	10	effect	effect	NOUN
ejpam-6387	109	11	of	of	ADP
ejpam-6387	109	12	the	the	DET
ejpam-6387	109	13	constant	constant	ADJ
ejpam-6387	109	14	c	c	NOUN
ejpam-6387	109	15	in	in	ADP
ejpam-6387	109	16	the	the	DET
ejpam-6387	109	17	order	order	NOUN
ejpam-6387	109	18	of	of	ADP
ejpam-6387	109	19	beurling	beurle	VERB
ejpam-6387	109	20	zeta	zeta	NOUN
ejpam-6387	109	21	function	function	NOUN
ejpam-6387	109	22	on	on	ADP
ejpam-6387	109	23	the	the	DET
ejpam-6387	109	24	upper	upper	ADJ
ejpam-6387	109	25	bound	bound	NOUN
ejpam-6387	109	26	of	of	ADP
ejpam-6387	109	27	np(x	np(x	NOUN
ejpam-6387	109	28	)	)	PUNCT
ejpam-6387	109	29	.	.	PUNCT
ejpam-6387	110	1	z.	z.	PROPN
ejpam-6387	110	2	m.	m.	PROPN
ejpam-6387	110	3	amen	amen	INTJ
ejpam-6387	110	4	,	,	PUNCT
ejpam-6387	110	5	f.	f.	PROPN
ejpam-6387	110	6	a.	a.	PROPN
ejpam-6387	110	7	al	al	PROPN
ejpam-6387	110	8	-	-	PUNCT
ejpam-6387	110	9	maamori	maamori	PROPN
ejpam-6387	110	10	,	,	PUNCT
ejpam-6387	110	11	m.	m.	NOUN
ejpam-6387	110	12	f.	f.	PROPN
ejpam-6387	110	13	hama	hama	PROPN
ejpam-6387	110	14	/	/	SYM
ejpam-6387	110	15	eur	eur	PROPN
ejpam-6387	110	16	.	.	PUNCT
ejpam-6387	111	1	j.	j.	PROPN
ejpam-6387	111	2	pure	pure	PROPN
ejpam-6387	111	3	appl	appl	PROPN
ejpam-6387	111	4	.	.	PROPN
ejpam-6387	111	5	math	math	PROPN
ejpam-6387	111	6	,	,	PUNCT
ejpam-6387	111	7	18	18	NUM
ejpam-6387	111	8	(	(	PUNCT
ejpam-6387	111	9	4	4	NUM
ejpam-6387	111	10	)	)	PUNCT
ejpam-6387	111	11	(	(	PUNCT
ejpam-6387	111	12	2025	2025	NUM
ejpam-6387	111	13	)	)	PUNCT
ejpam-6387	111	14	,	,	PUNCT
ejpam-6387	111	15	6387	6387	NUM
ejpam-6387	111	16	6	6	NUM
ejpam-6387	111	17	of	of	ADP
ejpam-6387	111	18	15	15	NUM
ejpam-6387	111	19	4	4	NUM
ejpam-6387	111	20	.	.	PUNCT
ejpam-6387	112	1	the	the	DET
ejpam-6387	112	2	effect	effect	NOUN
ejpam-6387	112	3	of	of	ADP
ejpam-6387	112	4	the	the	DET
ejpam-6387	112	5	constant	constant	ADJ
ejpam-6387	112	6	c	c	NOUN
ejpam-6387	112	7	on	on	ADP
ejpam-6387	112	8	the	the	DET
ejpam-6387	112	9	upper	upper	ADJ
ejpam-6387	112	10	bound	bind	VERB
ejpam-6387	112	11	of	of	ADP
ejpam-6387	112	12	generalised	generalised	ADJ
ejpam-6387	112	13	integr	integr	NOUN
ejpam-6387	112	14	counting	count	VERB
ejpam-6387	112	15	function	function	NOUN
ejpam-6387	112	16	np(x	np(x	NOUN
ejpam-6387	112	17	)	)	PUNCT
ejpam-6387	112	18	this	this	DET
ejpam-6387	112	19	work	work	NOUN
ejpam-6387	112	20	is	be	AUX
ejpam-6387	112	21	studying	study	VERB
ejpam-6387	112	22	the	the	DET
ejpam-6387	112	23	behavior	behavior	NOUN
ejpam-6387	112	24	of	of	ADP
ejpam-6387	112	25	np(x	np(x	NOUN
ejpam-6387	112	26	)	)	PUNCT
ejpam-6387	112	27	when	when	SCONJ
ejpam-6387	112	28	beurling	beurle	VERB
ejpam-6387	112	29	zeta	zeta	NOUN
ejpam-6387	112	30	function	function	NOUN
ejpam-6387	112	31	ζp(s	ζp(s	NOUN
ejpam-6387	112	32	)	)	PUNCT
ejpam-6387	112	33	has	have	AUX
ejpam-6387	112	34	known	know	VERB
ejpam-6387	112	35	asymptotic	asymptotic	ADJ
ejpam-6387	112	36	behavior	behavior	NOUN
ejpam-6387	112	37	.	.	PUNCT
ejpam-6387	113	1	there	there	PRON
ejpam-6387	113	2	is	be	VERB
ejpam-6387	113	3	no	no	DET
ejpam-6387	113	4	loss	loss	NOUN
ejpam-6387	113	5	of	of	ADP
ejpam-6387	113	6	generality	generality	NOUN
ejpam-6387	113	7	if	if	SCONJ
ejpam-6387	113	8	we	we	PRON
ejpam-6387	113	9	rewrite	rewrite	VERB
ejpam-6387	113	10	the	the	DET
ejpam-6387	113	11	statement	statement	NOUN
ejpam-6387	113	12	of	of	ADP
ejpam-6387	113	13	the	the	DET
ejpam-6387	113	14	theorem(1	theorem(1	NOUN
ejpam-6387	113	15	)	)	PUNCT
ejpam-6387	113	16	above	above	ADP
ejpam-6387	113	17	in	in	ADP
ejpam-6387	113	18	another	another	DET
ejpam-6387	113	19	style	style	NOUN
ejpam-6387	113	20	:	:	PUNCT
ejpam-6387	113	21	(	(	PUNCT
ejpam-6387	113	22	i	i	NOUN
ejpam-6387	113	23	)	)	PUNCT
ejpam-6387	113	24	suppose	suppose	VERB
ejpam-6387	113	25	for	for	ADP
ejpam-6387	113	26	some	some	DET
ejpam-6387	113	27	α	α	NOUN
ejpam-6387	113	28	∈	∈	PROPN
ejpam-6387	113	29	(	(	PUNCT
ejpam-6387	113	30	0	0	NUM
ejpam-6387	113	31	,	,	PUNCT
ejpam-6387	113	32	1	1	NUM
ejpam-6387	113	33	)	)	PUNCT
ejpam-6387	113	34	.	.	PUNCT
ejpam-6387	114	1	(	(	PUNCT
ejpam-6387	114	2	ii	ii	NOUN
ejpam-6387	114	3	)	)	PUNCT
ejpam-6387	114	4	ζp(s	ζp(s	NUM
ejpam-6387	114	5	)	)	PUNCT
ejpam-6387	114	6	has	have	VERB
ejpam-6387	114	7	an	an	DET
ejpam-6387	114	8	analytic	analytic	ADJ
ejpam-6387	114	9	continuation	continuation	NOUN
ejpam-6387	114	10	to	to	ADP
ejpam-6387	114	11	the	the	DET
ejpam-6387	114	12	half	half	ADJ
ejpam-6387	114	13	plane	plane	NOUN
ejpam-6387	114	14	hα	hα	VERB
ejpam-6387	114	15	except	except	SCONJ
ejpam-6387	114	16	for	for	ADP
ejpam-6387	114	17	a	a	DET
ejpam-6387	114	18	simple	simple	ADJ
ejpam-6387	114	19	pole	pole	NOUN
ejpam-6387	114	20	at	at	ADP
ejpam-6387	114	21	s	s	NOUN
ejpam-6387	114	22	=	=	NOUN
ejpam-6387	114	23	1	1	NUM
ejpam-6387	114	24	with	with	ADP
ejpam-6387	114	25	residue	residue	NOUN
ejpam-6387	114	26	β	β	NOUN
ejpam-6387	114	27	.	.	PUNCT
ejpam-6387	115	1	(	(	PUNCT
ejpam-6387	115	2	iii	iii	NOUN
ejpam-6387	115	3	)	)	PUNCT
ejpam-6387	115	4	for	for	ADP
ejpam-6387	115	5	some	some	DET
ejpam-6387	115	6	c	c	NOUN
ejpam-6387	115	7	<	<	X
ejpam-6387	115	8	1	1	NUM
ejpam-6387	115	9	,	,	PUNCT
ejpam-6387	115	10	we	we	PRON
ejpam-6387	115	11	have	have	VERB
ejpam-6387	115	12	ζp(σ	ζp(σ	X
ejpam-6387	115	13	+	+	CCONJ
ejpam-6387	115	14	it	it	PRON
ejpam-6387	115	15	)	)	PUNCT
ejpam-6387	116	1	=	=	PUNCT
ejpam-6387	116	2	o(tc	o(tc	NUM
ejpam-6387	116	3	)	)	PUNCT
ejpam-6387	116	4	,	,	PUNCT
ejpam-6387	116	5	for	for	ADP
ejpam-6387	116	6	some	some	DET
ejpam-6387	116	7	σ	σ	PROPN
ejpam-6387	116	8	≥	≥	NOUN
ejpam-6387	116	9	1−	1−	NUM
ejpam-6387	116	10	1	1	NUM
ejpam-6387	116	11	f(log	f(log	PROPN
ejpam-6387	116	12	t	t	PROPN
ejpam-6387	116	13	)	)	PUNCT
ejpam-6387	116	14	with	with	ADP
ejpam-6387	116	15	f	f	PROPN
ejpam-6387	116	16	is	be	AUX
ejpam-6387	116	17	positive	positive	ADJ
ejpam-6387	116	18	,	,	PUNCT
ejpam-6387	116	19	strictly	strictly	ADV
ejpam-6387	116	20	increasing	increase	VERB
ejpam-6387	116	21	continuous	continuous	ADJ
ejpam-6387	116	22	function	function	NOUN
ejpam-6387	116	23	,	,	PUNCT
ejpam-6387	116	24	tending	tend	VERB
ejpam-6387	116	25	to	to	ADP
ejpam-6387	116	26	infinity	infinity	NOUN
ejpam-6387	116	27	.	.	PUNCT
ejpam-6387	117	1	(	(	PUNCT
ejpam-6387	117	2	iv	iv	X
ejpam-6387	117	3	)	)	PUNCT
ejpam-6387	117	4	then	then	ADV
ejpam-6387	117	5	for	for	ADP
ejpam-6387	117	6	γ	γ	X
ejpam-6387	117	7	=	=	SYM
ejpam-6387	117	8	1−	1−	NUM
ejpam-6387	117	9	c	c	NOUN
ejpam-6387	117	10	,	,	PUNCT
ejpam-6387	117	11	np(x	np(x	NUM
ejpam-6387	117	12	)	)	PUNCT
ejpam-6387	117	13	=	=	SYM
ejpam-6387	118	1	βx+o(xe−	βx+o(xe−	PROPN
ejpam-6387	118	2	γ	γ	X
ejpam-6387	118	3	2	2	NUM
ejpam-6387	118	4	h−1(γ−1	h−1(γ−1	PROPN
ejpam-6387	118	5	log	log	NOUN
ejpam-6387	118	6	x	x	NOUN
ejpam-6387	118	7	)	)	PUNCT
ejpam-6387	118	8	)	)	PUNCT
ejpam-6387	118	9	where	where	SCONJ
ejpam-6387	118	10	h(u	h(u	NOUN
ejpam-6387	118	11	)	)	PUNCT
ejpam-6387	118	12	=	=	SYM
ejpam-6387	118	13	uf(u	uf(u	NUM
ejpam-6387	118	14	)	)	PUNCT
ejpam-6387	118	15	.	.	PUNCT
ejpam-6387	119	1	our	our	PRON
ejpam-6387	119	2	aim	aim	NOUN
ejpam-6387	119	3	here	here	ADV
ejpam-6387	119	4	is	be	AUX
ejpam-6387	119	5	to	to	PART
ejpam-6387	119	6	show	show	VERB
ejpam-6387	119	7	the	the	DET
ejpam-6387	119	8	effect	effect	NOUN
ejpam-6387	119	9	of	of	ADP
ejpam-6387	119	10	the	the	DET
ejpam-6387	119	11	constant	constant	ADJ
ejpam-6387	119	12	c	c	NOUN
ejpam-6387	119	13	appearing	appear	VERB
ejpam-6387	119	14	in	in	ADP
ejpam-6387	119	15	the	the	DET
ejpam-6387	119	16	order	order	NOUN
ejpam-6387	119	17	of	of	ADP
ejpam-6387	119	18	beurling	beurle	VERB
ejpam-6387	119	19	zeta	zeta	NOUN
ejpam-6387	119	20	function	function	NOUN
ejpam-6387	119	21	on	on	ADP
ejpam-6387	119	22	the	the	DET
ejpam-6387	119	23	error	error	NOUN
ejpam-6387	119	24	term	term	NOUN
ejpam-6387	119	25	of	of	ADP
ejpam-6387	119	26	np(x	np(x	NOUN
ejpam-6387	119	27	)	)	PUNCT
ejpam-6387	119	28	.	.	PUNCT
ejpam-6387	120	1	for	for	ADP
ejpam-6387	120	2	instance	instance	NOUN
ejpam-6387	120	3	assume	assume	VERB
ejpam-6387	120	4	that	that	SCONJ
ejpam-6387	120	5	theorem(1	theorem(1	NOUN
ejpam-6387	120	6	)	)	PUNCT
ejpam-6387	120	7	exist	exist	VERB
ejpam-6387	120	8	for	for	ADP
ejpam-6387	120	9	c	c	NOUN
ejpam-6387	120	10	=	=	SYM
ejpam-6387	120	11	1	1	NUM
ejpam-6387	120	12	2	2	NUM
ejpam-6387	120	13	.	.	PUNCT
ejpam-6387	121	1	its	its	PRON
ejpam-6387	121	2	worthwhile	worthwhile	NOUN
ejpam-6387	121	3	to	to	PART
ejpam-6387	121	4	mention	mention	VERB
ejpam-6387	121	5	that	that	SCONJ
ejpam-6387	121	6	we	we	PRON
ejpam-6387	121	7	adapted	adapt	VERB
ejpam-6387	121	8	the	the	DET
ejpam-6387	121	9	same	same	ADJ
ejpam-6387	121	10	strategy	strategy	NOUN
ejpam-6387	121	11	of	of	ADP
ejpam-6387	121	12	the	the	DET
ejpam-6387	121	13	proof	proof	NOUN
ejpam-6387	121	14	mentioned	mention	VERB
ejpam-6387	121	15	in	in	ADP
ejpam-6387	121	16	[	[	X
ejpam-6387	121	17	20	20	NUM
ejpam-6387	121	18	,	,	PUNCT
ejpam-6387	121	19	theorem	theorem	VERB
ejpam-6387	121	20	2.1,p	2.1,p	NUM
ejpam-6387	121	21	387	387	NUM
ejpam-6387	121	22	]	]	PUNCT
ejpam-6387	121	23	,	,	PUNCT
ejpam-6387	121	24	for	for	ADP
ejpam-6387	121	25	the	the	DET
ejpam-6387	121	26	purpose	purpose	NOUN
ejpam-6387	121	27	of	of	ADP
ejpam-6387	121	28	this	this	DET
ejpam-6387	121	29	work	work	NOUN
ejpam-6387	121	30	.	.	PUNCT
ejpam-6387	122	1	it	it	PRON
ejpam-6387	122	2	is	be	AUX
ejpam-6387	122	3	more	more	ADV
ejpam-6387	122	4	clear	clear	ADJ
ejpam-6387	122	5	to	to	PART
ejpam-6387	122	6	rewrite	rewrite	VERB
ejpam-6387	122	7	the	the	DET
ejpam-6387	122	8	theorem	theorem	NOUN
ejpam-6387	122	9	(	(	PUNCT
ejpam-6387	122	10	1	1	NUM
ejpam-6387	122	11	)	)	PUNCT
ejpam-6387	122	12	with	with	ADP
ejpam-6387	122	13	c	c	NOUN
ejpam-6387	122	14	=	=	SYM
ejpam-6387	122	15	1	1	NUM
ejpam-6387	122	16	2	2	NUM
ejpam-6387	122	17	and	and	CCONJ
ejpam-6387	122	18	one	one	NUM
ejpam-6387	122	19	can	can	AUX
ejpam-6387	122	20	see	see	VERB
ejpam-6387	122	21	how	how	SCONJ
ejpam-6387	122	22	the	the	DET
ejpam-6387	122	23	error	error	NOUN
ejpam-6387	122	24	term	term	NOUN
ejpam-6387	122	25	give	give	VERB
ejpam-6387	122	26	different	different	ADJ
ejpam-6387	122	27	result	result	NOUN
ejpam-6387	122	28	.	.	PUNCT
ejpam-6387	123	1	theorem	theorem	NOUN
ejpam-6387	123	2	2	2	NUM
ejpam-6387	123	3	.	.	PUNCT
ejpam-6387	123	4	suppose	suppose	VERB
ejpam-6387	123	5	that	that	SCONJ
ejpam-6387	123	6	for	for	ADP
ejpam-6387	123	7	some	some	DET
ejpam-6387	123	8	α	α	NOUN
ejpam-6387	123	9	∈	∈	PROPN
ejpam-6387	123	10	(	(	PUNCT
ejpam-6387	123	11	0	0	NUM
ejpam-6387	123	12	,	,	PUNCT
ejpam-6387	123	13	1	1	NUM
ejpam-6387	123	14	)	)	PUNCT
ejpam-6387	123	15	,	,	PUNCT
ejpam-6387	123	16	ζp(s	ζp(s	NUM
ejpam-6387	123	17	)	)	PUNCT
ejpam-6387	123	18	has	have	VERB
ejpam-6387	123	19	an	an	DET
ejpam-6387	123	20	analytic	analytic	ADJ
ejpam-6387	123	21	continuation	continuation	NOUN
ejpam-6387	123	22	to	to	ADP
ejpam-6387	123	23	the	the	DET
ejpam-6387	123	24	half	half	ADJ
ejpam-6387	123	25	plane	plane	NOUN
ejpam-6387	123	26	hα	hα	VERB
ejpam-6387	123	27	except	except	SCONJ
ejpam-6387	123	28	for	for	ADP
ejpam-6387	123	29	a	a	DET
ejpam-6387	123	30	simple	simple	ADJ
ejpam-6387	123	31	pole	pole	NOUN
ejpam-6387	123	32	at	at	ADP
ejpam-6387	123	33	s	s	NOUN
ejpam-6387	123	34	=	=	NOUN
ejpam-6387	123	35	1	1	NUM
ejpam-6387	123	36	with	with	ADP
ejpam-6387	123	37	residue	residue	NOUN
ejpam-6387	123	38	β	β	NOUN
ejpam-6387	123	39	.	.	PUNCT
ejpam-6387	124	1	further	far	ADV
ejpam-6387	124	2	assume	assume	VERB
ejpam-6387	124	3	that	that	SCONJ
ejpam-6387	124	4	for	for	ADP
ejpam-6387	124	5	some	some	DET
ejpam-6387	124	6	c	c	NOUN
ejpam-6387	124	7	<	<	X
ejpam-6387	124	8	1	1	NUM
ejpam-6387	124	9	ζp(σ	ζp(σ	NUM
ejpam-6387	124	10	+	+	CCONJ
ejpam-6387	124	11	it	it	PRON
ejpam-6387	124	12	)	)	PUNCT
ejpam-6387	125	1	=	=	PUNCT
ejpam-6387	126	1	o(t	o(t	NOUN
ejpam-6387	126	2	1	1	NUM
ejpam-6387	126	3	2	2	NUM
ejpam-6387	126	4	)	)	PUNCT
ejpam-6387	126	5	,	,	PUNCT
ejpam-6387	126	6	for	for	ADP
ejpam-6387	126	7	some	some	DET
ejpam-6387	126	8	σ	σ	PROPN
ejpam-6387	126	9	≥	≥	NOUN
ejpam-6387	126	10	1−	1−	NUM
ejpam-6387	126	11	1	1	NUM
ejpam-6387	126	12	f(log	f(log	PROPN
ejpam-6387	126	13	t	t	PROPN
ejpam-6387	126	14	)	)	PUNCT
ejpam-6387	126	15	where	where	SCONJ
ejpam-6387	126	16	f	f	PROPN
ejpam-6387	126	17	is	be	AUX
ejpam-6387	126	18	positive	positive	ADJ
ejpam-6387	126	19	,	,	PUNCT
ejpam-6387	126	20	strictly	strictly	ADV
ejpam-6387	126	21	increasing	increase	VERB
ejpam-6387	126	22	continuous	continuous	ADJ
ejpam-6387	126	23	function	function	NOUN
ejpam-6387	126	24	,	,	PUNCT
ejpam-6387	126	25	tending	tend	VERB
ejpam-6387	126	26	to	to	ADP
ejpam-6387	126	27	infinity	infinity	NOUN
ejpam-6387	126	28	.	.	PUNCT
ejpam-6387	127	1	then	then	ADV
ejpam-6387	127	2	for	for	ADP
ejpam-6387	127	3	γ	γ	X
ejpam-6387	127	4	=	=	SYM
ejpam-6387	127	5	1	1	NUM
ejpam-6387	127	6	2	2	NUM
ejpam-6387	127	7	,	,	PUNCT
ejpam-6387	127	8	np(x	np(x	NUM
ejpam-6387	127	9	)	)	PUNCT
ejpam-6387	127	10	=	=	SYM
ejpam-6387	127	11	βx+o	βx+o	PROPN
ejpam-6387	127	12	(	(	PUNCT
ejpam-6387	127	13	x	x	SYM
ejpam-6387	127	14	exp	exp	NOUN
ejpam-6387	127	15	(	(	PUNCT
ejpam-6387	127	16	−1	−1	NOUN
ejpam-6387	127	17	4	4	NUM
ejpam-6387	127	18	h−1(2	h−1(2	NOUN
ejpam-6387	127	19	log	log	NOUN
ejpam-6387	127	20	x	x	NOUN
ejpam-6387	127	21	)	)	PUNCT
ejpam-6387	127	22	)	)	PUNCT
ejpam-6387	127	23	)	)	PUNCT
ejpam-6387	127	24	where	where	SCONJ
ejpam-6387	127	25	h(u	h(u	NOUN
ejpam-6387	127	26	)	)	PUNCT
ejpam-6387	127	27	=	=	SYM
ejpam-6387	127	28	uf(u	uf(u	NUM
ejpam-6387	127	29	)	)	PUNCT
ejpam-6387	127	30	.	.	PUNCT
ejpam-6387	128	1	proof	proof	NOUN
ejpam-6387	128	2	.	.	PUNCT
ejpam-6387	129	1	by	by	ADP
ejpam-6387	129	2	given	give	VERB
ejpam-6387	129	3	assume	assume	VERB
ejpam-6387	129	4	that	that	SCONJ
ejpam-6387	129	5	the	the	DET
ejpam-6387	129	6	upper	upper	ADJ
ejpam-6387	129	7	bound	bound	NOUN
ejpam-6387	129	8	of	of	ADP
ejpam-6387	129	9	ζp(s	ζp(s	NOUN
ejpam-6387	129	10	)	)	PUNCT
ejpam-6387	129	11	=	=	PUNCT
ejpam-6387	129	12	o(t	o(t	NOUN
ejpam-6387	129	13	1	1	NUM
ejpam-6387	129	14	2	2	NUM
ejpam-6387	129	15	)	)	PUNCT
ejpam-6387	129	16	,	,	PUNCT
ejpam-6387	129	17	and	and	CCONJ
ejpam-6387	129	18	to	to	PART
ejpam-6387	129	19	find	find	VERB
ejpam-6387	129	20	approximate	approximate	ADJ
ejpam-6387	129	21	formula	formula	NOUN
ejpam-6387	129	22	for	for	ADP
ejpam-6387	129	23	zp(x	zp(x	NUM
ejpam-6387	129	24	)	)	PUNCT
ejpam-6387	129	25	.	.	PUNCT
ejpam-6387	130	1	we	we	PRON
ejpam-6387	130	2	know	know	VERB
ejpam-6387	130	3	by	by	ADP
ejpam-6387	130	4	perron	perron	PROPN
ejpam-6387	130	5	’s	’s	PART
ejpam-6387	130	6	formula	formula	NOUN
ejpam-6387	130	7	[	[	X
ejpam-6387	130	8	21	21	NUM
ejpam-6387	130	9	]	]	PUNCT
ejpam-6387	130	10	,	,	PUNCT
ejpam-6387	130	11	np(y	np(y	X
ejpam-6387	130	12	)	)	PUNCT
ejpam-6387	130	13	=	=	SYM
ejpam-6387	131	1	1	1	NUM
ejpam-6387	131	2	2πi	2πi	ADJ
ejpam-6387	131	3	∫	∫	PROPN
ejpam-6387	131	4	b+i∞	b+i∞	PROPN
ejpam-6387	131	5	b−i∞	b−i∞	PROPN
ejpam-6387	131	6	ζp(s)y	ζp(s)y	PROPN
ejpam-6387	131	7	s	s	PART
ejpam-6387	131	8	s	s	X
ejpam-6387	131	9	ds	d	NOUN
ejpam-6387	131	10	,	,	PUNCT
ejpam-6387	131	11	where	where	SCONJ
ejpam-6387	131	12	b	b	X
ejpam-6387	131	13	>	>	X
ejpam-6387	131	14	1	1	NUM
ejpam-6387	131	15	z.	z.	PROPN
ejpam-6387	131	16	m.	m.	NOUN
ejpam-6387	131	17	amen	amen	PROPN
ejpam-6387	131	18	,	,	PUNCT
ejpam-6387	131	19	f.	f.	PROPN
ejpam-6387	131	20	a.	a.	PROPN
ejpam-6387	131	21	al	al	PROPN
ejpam-6387	131	22	-	-	PUNCT
ejpam-6387	131	23	maamori	maamori	PROPN
ejpam-6387	131	24	,	,	PUNCT
ejpam-6387	131	25	m.	m.	NOUN
ejpam-6387	131	26	f.	f.	PROPN
ejpam-6387	131	27	hama	hama	PROPN
ejpam-6387	131	28	/	/	SYM
ejpam-6387	131	29	eur	eur	PROPN
ejpam-6387	131	30	.	.	PUNCT
ejpam-6387	132	1	j.	j.	PROPN
ejpam-6387	132	2	pure	pure	PROPN
ejpam-6387	132	3	appl	appl	PROPN
ejpam-6387	132	4	.	.	PROPN
ejpam-6387	132	5	math	math	PROPN
ejpam-6387	132	6	,	,	PUNCT
ejpam-6387	132	7	18	18	NUM
ejpam-6387	132	8	(	(	PUNCT
ejpam-6387	132	9	4	4	NUM
ejpam-6387	132	10	)	)	PUNCT
ejpam-6387	132	11	(	(	PUNCT
ejpam-6387	132	12	2025	2025	NUM
ejpam-6387	132	13	)	)	PUNCT
ejpam-6387	132	14	,	,	PUNCT
ejpam-6387	132	15	6387	6387	NUM
ejpam-6387	132	16	7	7	NUM
ejpam-6387	132	17	of	of	ADP
ejpam-6387	132	18	15	15	NUM
ejpam-6387	132	19	zp(x	zp(x	NUM
ejpam-6387	132	20	)	)	PUNCT
ejpam-6387	132	21	=	=	SYM
ejpam-6387	133	1	∫	∫	PUNCT
ejpam-6387	133	2	x	x	SYM
ejpam-6387	133	3	0	0	NUM
ejpam-6387	133	4	np(y)dy	np(y)dy	NOUN
ejpam-6387	133	5	=	=	SYM
ejpam-6387	133	6	∫	∫	PROPN
ejpam-6387	133	7	x	x	SYM
ejpam-6387	133	8	0	0	PROPN
ejpam-6387	133	9	(	(	PUNCT
ejpam-6387	133	10	1	1	NUM
ejpam-6387	133	11	2πi	2πi	ADJ
ejpam-6387	133	12	∫	∫	PROPN
ejpam-6387	133	13	b+i∞	b+i∞	PROPN
ejpam-6387	133	14	b−i∞	b−i∞	PROPN
ejpam-6387	133	15	ζp(s)y	ζp(s)y	PROPN
ejpam-6387	133	16	s	s	PART
ejpam-6387	133	17	s	s	X
ejpam-6387	133	18	ds	ds	ADJ
ejpam-6387	133	19	)	)	PUNCT
ejpam-6387	133	20	dy	dy	NOUN
ejpam-6387	133	21	=	=	SYM
ejpam-6387	133	22	1	1	NUM
ejpam-6387	133	23	2πi	2πi	ADJ
ejpam-6387	133	24	∫	∫	PROPN
ejpam-6387	133	25	b+i∞	b+i∞	PROPN
ejpam-6387	133	26	b−i∞	b−i∞	PROPN
ejpam-6387	133	27	ζp(s)x	ζp(s)x	PROPN
ejpam-6387	133	28	s+1	s+1	NUM
ejpam-6387	133	29	s(s+	s(s+	VERB
ejpam-6387	133	30	1	1	NUM
ejpam-6387	133	31	)	)	PUNCT
ejpam-6387	133	32	ds	ds	PROPN
ejpam-6387	133	33	,	,	PUNCT
ejpam-6387	133	34	b	b	NOUN
ejpam-6387	133	35	>	>	X
ejpam-6387	133	36	1	1	NUM
ejpam-6387	133	37	pushing	push	VERB
ejpam-6387	133	38	the	the	DET
ejpam-6387	133	39	contour	contour	NOUN
ejpam-6387	133	40	to	to	ADP
ejpam-6387	133	41	the	the	DET
ejpam-6387	133	42	left	left	NOUN
ejpam-6387	133	43	of	of	ADP
ejpam-6387	133	44	the	the	DET
ejpam-6387	133	45	line	line	NOUN
ejpam-6387	133	46	re(s	re(s	PUNCT
ejpam-6387	133	47	)	)	PUNCT
ejpam-6387	134	1	=	=	SYM
ejpam-6387	134	2	b	b	X
ejpam-6387	134	3	past	past	ADP
ejpam-6387	134	4	the	the	DET
ejpam-6387	134	5	simple	simple	ADJ
ejpam-6387	134	6	pole	pole	NOUN
ejpam-6387	134	7	at	at	ADP
ejpam-6387	134	8	s	s	NOUN
ejpam-6387	134	9	=	=	SYM
ejpam-6387	134	10	1	1	NUM
ejpam-6387	134	11	,	,	PUNCT
ejpam-6387	134	12	we	we	PRON
ejpam-6387	134	13	get	get	VERB
ejpam-6387	134	14	for	for	ADP
ejpam-6387	134	15	any	any	DET
ejpam-6387	134	16	t	t	NOUN
ejpam-6387	134	17	>	>	X
ejpam-6387	134	18	0	0	NUM
ejpam-6387	134	19	zp(x	zp(x	NUM
ejpam-6387	134	20	)	)	PUNCT
ejpam-6387	134	21	=	=	PUNCT
ejpam-6387	135	1	β	β	X
ejpam-6387	135	2	2	2	NUM
ejpam-6387	135	3	x2	x2	NOUN
ejpam-6387	136	1	+	+	CCONJ
ejpam-6387	136	2	1	1	NUM
ejpam-6387	136	3	2πi	2πi	ADJ
ejpam-6387	136	4	∫	∫	NOUN
ejpam-6387	136	5	λt	λt	ADP
ejpam-6387	136	6	ζp(s	ζp(s	NOUN
ejpam-6387	136	7	)	)	PUNCT
ejpam-6387	136	8	xs+1	xs+1	NOUN
ejpam-6387	136	9	s(s+	s(s+	VERB
ejpam-6387	136	10	1	1	NUM
ejpam-6387	136	11	)	)	PUNCT
ejpam-6387	136	12	ds+	ds+	NOUN
ejpam-6387	137	1	1	1	NUM
ejpam-6387	137	2	2πi	2πi	NOUN
ejpam-6387	137	3	∫	∫	PROPN
ejpam-6387	137	4	b+it	b+it	NOUN
ejpam-6387	137	5	1−	1−	NUM
ejpam-6387	137	6	1	1	NUM
ejpam-6387	137	7	f(logt	f(logt	NOUN
ejpam-6387	137	8	)	)	PUNCT
ejpam-6387	138	1	+	+	ADP
ejpam-6387	138	2	it	it	PRON
ejpam-6387	138	3	ζp(s	ζp(s	NOUN
ejpam-6387	138	4	)	)	PUNCT
ejpam-6387	138	5	xs+1	xs+1	NOUN
ejpam-6387	138	6	s(s+	s(s+	VERB
ejpam-6387	138	7	1	1	NUM
ejpam-6387	138	8	)	)	PUNCT
ejpam-6387	138	9	ds	ds	NOUN
ejpam-6387	139	1	+	+	NOUN
ejpam-6387	139	2	1	1	NUM
ejpam-6387	139	3	2πi	2πi	ADJ
ejpam-6387	139	4	∫	∫	PROPN
ejpam-6387	139	5	1−	1−	NUM
ejpam-6387	139	6	1	1	NUM
ejpam-6387	139	7	f(logt	f(logt	NOUN
ejpam-6387	139	8	)	)	PUNCT
ejpam-6387	139	9	−it	−it	PROPN
ejpam-6387	139	10	b−it	b−it	X
ejpam-6387	139	11	ζp(s	ζp(s	NUM
ejpam-6387	139	12	)	)	PUNCT
ejpam-6387	139	13	xs+1	xs+1	NOUN
ejpam-6387	139	14	s(s+	s(s+	VERB
ejpam-6387	139	15	1	1	NUM
ejpam-6387	139	16	)	)	PUNCT
ejpam-6387	139	17	ds+	ds+	NOUN
ejpam-6387	139	18	1	1	NUM
ejpam-6387	139	19	2πi	2πi	NOUN
ejpam-6387	139	20	∫	∫	NOUN
ejpam-6387	139	21	b+i∞	b+i∞	ADJ
ejpam-6387	139	22	b+it	b+it	NOUN
ejpam-6387	139	23	ζp(s	ζp(s	NUM
ejpam-6387	139	24	)	)	PUNCT
ejpam-6387	139	25	xs+1	xs+1	NOUN
ejpam-6387	139	26	s(s+	s(s+	VERB
ejpam-6387	139	27	1	1	NUM
ejpam-6387	139	28	)	)	PUNCT
ejpam-6387	139	29	ds	ds	ADJ
ejpam-6387	139	30	(	(	PUNCT
ejpam-6387	139	31	2	2	NUM
ejpam-6387	139	32	)	)	PUNCT
ejpam-6387	139	33	figure	figure	NOUN
ejpam-6387	139	34	1	1	NUM
ejpam-6387	139	35	:	:	PUNCT
ejpam-6387	139	36	contour	contour	NOUN
ejpam-6387	139	37	λt	λt	ADP
ejpam-6387	139	38	here	here	ADV
ejpam-6387	139	39	λt	λt	ADP
ejpam-6387	139	40	is	be	AUX
ejpam-6387	139	41	the	the	DET
ejpam-6387	139	42	contour	contour	NOUN
ejpam-6387	139	43	s	s	NOUN
ejpam-6387	139	44	=	=	SYM
ejpam-6387	139	45	1−	1−	NUM
ejpam-6387	139	46	1	1	NUM
ejpam-6387	139	47	f(log	f(log	PROPN
ejpam-6387	139	48	t	t	PROPN
ejpam-6387	139	49	)	)	PUNCT
ejpam-6387	139	50	+	+	CCONJ
ejpam-6387	139	51	it	it	PRON
ejpam-6387	139	52	for	for	ADP
ejpam-6387	139	53	a	a	DET
ejpam-6387	139	54	<	<	X
ejpam-6387	139	55	|t|	|t|	PROPN
ejpam-6387	139	56	≤	≤	ADJ
ejpam-6387	139	57	t	t	PROPN
ejpam-6387	139	58	and	and	CCONJ
ejpam-6387	139	59	s	s	X
ejpam-6387	139	60	=	=	SYM
ejpam-6387	139	61	1−	1−	NUM
ejpam-6387	139	62	1	1	NUM
ejpam-6387	139	63	f(log	f(log	PROPN
ejpam-6387	139	64	a	a	PROPN
ejpam-6387	139	65	)	)	PUNCT
ejpam-6387	139	66	+	+	CCONJ
ejpam-6387	139	67	it	it	PRON
ejpam-6387	139	68	for	for	ADP
ejpam-6387	139	69	|t|	|t|	ADJ
ejpam-6387	139	70	≤	≤	NUM
ejpam-6387	139	71	a.	a.	NOUN
ejpam-6387	140	1	the	the	DET
ejpam-6387	140	2	constant	constant	ADJ
ejpam-6387	140	3	a	a	PRON
ejpam-6387	140	4	is	be	AUX
ejpam-6387	140	5	chosen	choose	VERB
ejpam-6387	140	6	such	such	ADJ
ejpam-6387	140	7	that	that	SCONJ
ejpam-6387	140	8	a	a	DET
ejpam-6387	140	9	>	>	X
ejpam-6387	140	10	e	e	NOUN
ejpam-6387	140	11	and	and	CCONJ
ejpam-6387	140	12	1−	1−	NUM
ejpam-6387	140	13	1	1	NUM
ejpam-6387	140	14	f(log	f(log	PROPN
ejpam-6387	140	15	a	a	PROPN
ejpam-6387	140	16	)	)	PUNCT
ejpam-6387	141	1	>	>	X
ejpam-6387	141	2	α	α	X
ejpam-6387	141	3	.	.	PUNCT
ejpam-6387	142	1	the	the	DET
ejpam-6387	142	2	integration	integration	NOUN
ejpam-6387	142	3	of	of	ADP
ejpam-6387	142	4	the	the	DET
ejpam-6387	142	5	third	third	ADJ
ejpam-6387	142	6	term	term	NOUN
ejpam-6387	142	7	of	of	ADP
ejpam-6387	142	8	the	the	DET
ejpam-6387	142	9	equation	equation	NOUN
ejpam-6387	142	10	(	(	PUNCT
ejpam-6387	142	11	2	2	NUM
ejpam-6387	142	12	)	)	PUNCT
ejpam-6387	142	13	on	on	ADP
ejpam-6387	142	14	[	[	X
ejpam-6387	142	15	1	1	NUM
ejpam-6387	142	16	−	−	PROPN
ejpam-6387	142	17	1	1	NUM
ejpam-6387	142	18	f(log	f(log	PROPN
ejpam-6387	142	19	t	t	PROPN
ejpam-6387	142	20	)	)	PUNCT
ejpam-6387	142	21	+	+	CCONJ
ejpam-6387	142	22	it	it	PRON
ejpam-6387	142	23	,	,	PUNCT
ejpam-6387	142	24	b	b	X
ejpam-6387	143	1	+	+	CCONJ
ejpam-6387	143	2	it	it	PRON
ejpam-6387	143	3	]	]	PUNCT
ejpam-6387	143	4	is	be	AUX
ejpam-6387	143	5	equal	equal	ADJ
ejpam-6387	143	6	to	to	ADP
ejpam-6387	143	7	o	o	PROPN
ejpam-6387	143	8	(	(	PUNCT
ejpam-6387	143	9	xb+1	xb+1	NOUN
ejpam-6387	143	10	t	t	PROPN
ejpam-6387	143	11	3/2	3/2	NUM
ejpam-6387	143	12	log	log	NOUN
ejpam-6387	143	13	x	x	PUNCT
ejpam-6387	143	14	)	)	PUNCT
ejpam-6387	144	1	−→	−→	ADV
ejpam-6387	144	2	0	0	PUNCT
ejpam-6387	144	3	as	as	SCONJ
ejpam-6387	144	4	t	t	PROPN
ejpam-6387	144	5	−→	−→	NOUN
ejpam-6387	144	6	∞.	∞.	PROPN
ejpam-6387	144	7	similarily	similarily	ADV
ejpam-6387	144	8	the	the	DET
ejpam-6387	144	9	fourth	fourth	ADJ
ejpam-6387	144	10	term	term	NOUN
ejpam-6387	144	11	of	of	ADP
ejpam-6387	144	12	the	the	DET
ejpam-6387	144	13	a	a	DET
ejpam-6387	144	14	equation	equation	NOUN
ejpam-6387	144	15	(	(	PUNCT
ejpam-6387	144	16	2	2	X
ejpam-6387	144	17	)	)	PUNCT
ejpam-6387	144	18	is	be	AUX
ejpam-6387	144	19	also	also	ADV
ejpam-6387	144	20	0	0	NUM
ejpam-6387	144	21	when	when	SCONJ
ejpam-6387	144	22	t	t	PROPN
ejpam-6387	144	23	−→	−→	NOUN
ejpam-6387	144	24	∞.	∞.	PROPN
ejpam-6387	144	25	so	so	ADV
ejpam-6387	144	26	,	,	PUNCT
ejpam-6387	144	27	equation	equation	NOUN
ejpam-6387	144	28	(	(	PUNCT
ejpam-6387	144	29	2	2	X
ejpam-6387	144	30	)	)	PUNCT
ejpam-6387	144	31	becomes	become	VERB
ejpam-6387	144	32	zp(x	zp(x	NUM
ejpam-6387	144	33	)	)	PUNCT
ejpam-6387	144	34	=	=	PUNCT
ejpam-6387	145	1	β	β	X
ejpam-6387	145	2	2	2	NUM
ejpam-6387	145	3	x2	x2	NOUN
ejpam-6387	146	1	+	+	CCONJ
ejpam-6387	146	2	1	1	NUM
ejpam-6387	146	3	2πi	2πi	ADJ
ejpam-6387	146	4	∫	∫	NOUN
ejpam-6387	146	5	λt	λt	ADP
ejpam-6387	146	6	ζp(s	ζp(s	NOUN
ejpam-6387	146	7	)	)	PUNCT
ejpam-6387	146	8	xs+1	xs+1	NOUN
ejpam-6387	146	9	s(s+	s(s+	VERB
ejpam-6387	146	10	1	1	NUM
ejpam-6387	146	11	)	)	PUNCT
ejpam-6387	146	12	ds	ds	NOUN
ejpam-6387	146	13	where	where	SCONJ
ejpam-6387	146	14	λt	λt	ADV
ejpam-6387	146	15	is	be	AUX
ejpam-6387	146	16	the	the	DET
ejpam-6387	146	17	contour	contour	NOUN
ejpam-6387	146	18	s	s	NOUN
ejpam-6387	146	19	=	=	SYM
ejpam-6387	146	20	1	1	NUM
ejpam-6387	146	21	−	−	PROPN
ejpam-6387	146	22	1	1	NUM
ejpam-6387	146	23	f(log	f(log	PROPN
ejpam-6387	146	24	t	t	PROPN
ejpam-6387	146	25	)	)	PUNCT
ejpam-6387	146	26	+	+	CCONJ
ejpam-6387	146	27	it	it	PRON
ejpam-6387	146	28	for	for	ADP
ejpam-6387	146	29	|t|	|t|	PROPN
ejpam-6387	146	30	>	>	X
ejpam-6387	146	31	a	a	PRON
ejpam-6387	146	32	>	>	X
ejpam-6387	146	33	e	e	X
ejpam-6387	146	34	and	and	CCONJ
ejpam-6387	146	35	s	s	PART
ejpam-6387	146	36	=	=	SYM
ejpam-6387	146	37	1	1	NUM
ejpam-6387	146	38	−	−	PROPN
ejpam-6387	146	39	1	1	NUM
ejpam-6387	146	40	f(log	f(log	PROPN
ejpam-6387	146	41	a	a	NOUN
ejpam-6387	146	42	)	)	PUNCT
ejpam-6387	146	43	+	+	CCONJ
ejpam-6387	146	44	it	it	PRON
ejpam-6387	146	45	for	for	ADP
ejpam-6387	146	46	|t|	|t|	NOUN
ejpam-6387	146	47	<	<	X
ejpam-6387	146	48	a.	a.	PROPN
ejpam-6387	146	49	z.	z.	PROPN
ejpam-6387	146	50	m.	m.	PROPN
ejpam-6387	147	1	amen	amen	PROPN
ejpam-6387	147	2	,	,	PUNCT
ejpam-6387	147	3	f.	f.	PROPN
ejpam-6387	147	4	a.	a.	PROPN
ejpam-6387	147	5	al	al	PROPN
ejpam-6387	147	6	-	-	PUNCT
ejpam-6387	147	7	maamori	maamori	PROPN
ejpam-6387	147	8	,	,	PUNCT
ejpam-6387	147	9	m.	m.	NOUN
ejpam-6387	147	10	f.	f.	PROPN
ejpam-6387	147	11	hama	hama	PROPN
ejpam-6387	147	12	/	/	SYM
ejpam-6387	147	13	eur	eur	PROPN
ejpam-6387	147	14	.	.	PUNCT
ejpam-6387	148	1	j.	j.	PROPN
ejpam-6387	148	2	pure	pure	PROPN
ejpam-6387	148	3	appl	appl	PROPN
ejpam-6387	148	4	.	.	PROPN
ejpam-6387	148	5	math	math	PROPN
ejpam-6387	148	6	,	,	PUNCT
ejpam-6387	148	7	18	18	NUM
ejpam-6387	148	8	(	(	PUNCT
ejpam-6387	148	9	4	4	NUM
ejpam-6387	148	10	)	)	PUNCT
ejpam-6387	148	11	(	(	PUNCT
ejpam-6387	148	12	2025	2025	NUM
ejpam-6387	148	13	)	)	PUNCT
ejpam-6387	148	14	,	,	PUNCT
ejpam-6387	148	15	6387	6387	NUM
ejpam-6387	148	16	8	8	NUM
ejpam-6387	148	17	of	of	ADP
ejpam-6387	148	18	15	15	NUM
ejpam-6387	148	19	therefore,∣∣∣zp(x)−	therefore,∣∣∣zp(x)−	PROPN
ejpam-6387	148	20	β	β	X
ejpam-6387	148	21	2x	2x	NUM
ejpam-6387	148	22	2	2	NUM
ejpam-6387	148	23	∣∣∣	∣∣∣	NOUN
ejpam-6387	148	24	=	=	PUNCT
ejpam-6387	148	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6387	148	26	1	1	NUM
ejpam-6387	148	27	2πi	2πi	NOUN
ejpam-6387	148	28	∫	∫	NOUN
ejpam-6387	148	29	λt	λt	ADP
ejpam-6387	148	30	ζp(s	ζp(s	NOUN
ejpam-6387	148	31	)	)	PUNCT
ejpam-6387	148	32	xs+1	xs+1	PROPN
ejpam-6387	148	33	s(s+1)ds	s(s+1)ds	NOUN
ejpam-6387	148	34	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6387	148	35	=	=	SYM
ejpam-6387	148	36	o	o	PROPN
ejpam-6387	148	37	(	(	PUNCT
ejpam-6387	148	38	∫∞	∫∞	NOUN
ejpam-6387	148	39	a	a	DET
ejpam-6387	148	40	∣∣∣ζp(1−	∣∣∣ζp(1−	NUM
ejpam-6387	148	41	1	1	NUM
ejpam-6387	148	42	f(log	f(log	PROPN
ejpam-6387	148	43	t	t	PROPN
ejpam-6387	148	44	)	)	PUNCT
ejpam-6387	148	45	−it	−it	PROPN
ejpam-6387	148	46	)	)	PUNCT
ejpam-6387	148	47	∣∣∣	∣∣∣	NOUN
ejpam-6387	148	48	t2	t2	PROPN
ejpam-6387	148	49	.x	.x	NOUN
ejpam-6387	148	50	2−	2−	NUM
ejpam-6387	148	51	1	1	NUM
ejpam-6387	148	52	f(log	f(log	PROPN
ejpam-6387	148	53	t)dt	t)dt	PROPN
ejpam-6387	148	54	)	)	PUNCT
ejpam-6387	149	1	+	+	NOUN
ejpam-6387	149	2	o	o	X
ejpam-6387	149	3	(	(	PUNCT
ejpam-6387	149	4	x	x	SYM
ejpam-6387	149	5	2−	2−	NUM
ejpam-6387	149	6	1	1	NUM
ejpam-6387	149	7	f(log	f(log	PROPN
ejpam-6387	149	8	a	a	NOUN
ejpam-6387	149	9	)	)	PUNCT
ejpam-6387	149	10	)	)	PUNCT
ejpam-6387	150	1	=	=	PUNCT
ejpam-6387	150	2	o	o	X
ejpam-6387	150	3	(	(	PUNCT
ejpam-6387	150	4	x2	x2	PROPN
ejpam-6387	150	5	∫∞	∫∞	NOUN
ejpam-6387	150	6	log	log	VERB
ejpam-6387	150	7	a	a	DET
ejpam-6387	150	8	exp	exp	NOUN
ejpam-6387	150	9	[	[	PUNCT
ejpam-6387	150	10	log	log	NOUN
ejpam-6387	150	11	ζp(1−	ζp(1−	PROPN
ejpam-6387	150	12	1	1	NUM
ejpam-6387	150	13	f(log	f(log	PROPN
ejpam-6387	150	14	t	t	PROPN
ejpam-6387	150	15	)	)	PUNCT
ejpam-6387	150	16	−	−	PROPN
ejpam-6387	151	1	it)−	it)−	PROPN
ejpam-6387	151	2	log	log	NOUN
ejpam-6387	151	3	t2	t2	NOUN
ejpam-6387	151	4	+	+	CCONJ
ejpam-6387	151	5	log	log	NOUN
ejpam-6387	151	6	x	x	PUNCT
ejpam-6387	151	7	−	−	PROPN
ejpam-6387	151	8	1	1	NUM
ejpam-6387	151	9	f(log	f(log	PROPN
ejpam-6387	151	10	t)dt	t)dt	PROPN
ejpam-6387	151	11	]	]	PUNCT
ejpam-6387	151	12	)	)	PUNCT
ejpam-6387	152	1	+	+	NOUN
ejpam-6387	152	2	o	o	X
ejpam-6387	152	3	(	(	PUNCT
ejpam-6387	152	4	x	x	SYM
ejpam-6387	152	5	2−	2−	NUM
ejpam-6387	152	6	1	1	NUM
ejpam-6387	152	7	f(log	f(log	PROPN
ejpam-6387	152	8	a	a	NOUN
ejpam-6387	152	9	)	)	PUNCT
ejpam-6387	152	10	)	)	PUNCT
ejpam-6387	153	1	=	=	PUNCT
ejpam-6387	153	2	o	o	X
ejpam-6387	153	3	(	(	PUNCT
ejpam-6387	153	4	x2	x2	PROPN
ejpam-6387	153	5	∫∞	∫∞	NOUN
ejpam-6387	153	6	log	log	VERB
ejpam-6387	153	7	a	a	DET
ejpam-6387	153	8	exp	exp	NOUN
ejpam-6387	153	9	[	[	PUNCT
ejpam-6387	154	1	log	log	NOUN
ejpam-6387	154	2	t	t	PROPN
ejpam-6387	154	3	1/2	1/2	NUM
ejpam-6387	154	4	−	−	PROPN
ejpam-6387	154	5	2	2	NUM
ejpam-6387	154	6	log	log	NOUN
ejpam-6387	154	7	t	t	NOUN
ejpam-6387	154	8	−	−	PROPN
ejpam-6387	154	9	1	1	NUM
ejpam-6387	154	10	f(log	f(log	PROPN
ejpam-6387	154	11	t	t	PROPN
ejpam-6387	154	12	)	)	PUNCT
ejpam-6387	154	13	.	.	PUNCT
ejpam-6387	155	1	log	log	VERB
ejpam-6387	155	2	x	x	X
ejpam-6387	155	3	]	]	X
ejpam-6387	155	4	dt	dt	X
ejpam-6387	155	5	)	)	PUNCT
ejpam-6387	156	1	+	+	ADP
ejpam-6387	156	2	o	o	X
ejpam-6387	156	3	(	(	PUNCT
ejpam-6387	156	4	x	x	SYM
ejpam-6387	156	5	2−	2−	NUM
ejpam-6387	156	6	1	1	NUM
ejpam-6387	156	7	f(log	f(log	PROPN
ejpam-6387	156	8	a	a	NOUN
ejpam-6387	156	9	)	)	PUNCT
ejpam-6387	156	10	)	)	PUNCT
ejpam-6387	156	11	.	.	PUNCT
ejpam-6387	157	1	by	by	ADP
ejpam-6387	157	2	using	use	VERB
ejpam-6387	157	3	u	u	NOUN
ejpam-6387	157	4	=	=	PROPN
ejpam-6387	157	5	log	log	PROPN
ejpam-6387	157	6	t	t	PROPN
ejpam-6387	157	7	,	,	PUNCT
ejpam-6387	157	8	to	to	PART
ejpam-6387	157	9	get	get	VERB
ejpam-6387	157	10	:	:	PUNCT
ejpam-6387	157	11	=	=	SYM
ejpam-6387	157	12	o	o	X
ejpam-6387	157	13	(	(	PUNCT
ejpam-6387	157	14	x2	x2	NOUN
ejpam-6387	157	15	∫	∫	PROPN
ejpam-6387	157	16	∞	∞	PROPN
ejpam-6387	157	17	log	log	VERB
ejpam-6387	157	18	a	a	DET
ejpam-6387	157	19	exp	exp	NOUN
ejpam-6387	157	20	[	[	PUNCT
ejpam-6387	157	21	−	−	PROPN
ejpam-6387	157	22	(	(	PUNCT
ejpam-6387	157	23	1	1	NUM
ejpam-6387	157	24	2	2	NUM
ejpam-6387	157	25	u+	u+	NUM
ejpam-6387	157	26	log	log	NOUN
ejpam-6387	157	27	x	x	NOUN
ejpam-6387	157	28	f(u	f(u	PROPN
ejpam-6387	157	29	)	)	PUNCT
ejpam-6387	157	30	)	)	PUNCT
ejpam-6387	157	31	]	]	PUNCT
ejpam-6387	158	1	du	du	X
ejpam-6387	158	2	)	)	PUNCT
ejpam-6387	159	1	+	+	ADP
ejpam-6387	159	2	o	o	X
ejpam-6387	159	3	(	(	PUNCT
ejpam-6387	159	4	x	x	SYM
ejpam-6387	159	5	2−	2−	NUM
ejpam-6387	159	6	1	1	NUM
ejpam-6387	159	7	f(log	f(log	PROPN
ejpam-6387	159	8	a	a	NOUN
ejpam-6387	159	9	)	)	PUNCT
ejpam-6387	159	10	)	)	PUNCT
ejpam-6387	159	11	by	by	ADP
ejpam-6387	159	12	using	use	VERB
ejpam-6387	159	13	some	some	DET
ejpam-6387	159	14	manipulations	manipulation	NOUN
ejpam-6387	159	15	to	to	ADP
ejpam-6387	159	16	the	the	DET
ejpam-6387	159	17	above	above	ADJ
ejpam-6387	159	18	integral	integral	ADJ
ejpam-6387	159	19	to	to	ADP
ejpam-6387	159	20	get:∫	get:∫	PROPN
ejpam-6387	159	21	∞	∞	PROPN
ejpam-6387	159	22	loga	loga	NOUN
ejpam-6387	159	23	exp	exp	NOUN
ejpam-6387	159	24	[	[	PUNCT
ejpam-6387	159	25	−	−	PROPN
ejpam-6387	159	26	(	(	PUNCT
ejpam-6387	159	27	1	1	NUM
ejpam-6387	159	28	2	2	NUM
ejpam-6387	159	29	u+	u+	NOUN
ejpam-6387	159	30	logx	logx	NOUN
ejpam-6387	159	31	f(u	f(u	PROPN
ejpam-6387	159	32	)	)	PUNCT
ejpam-6387	159	33	)	)	PUNCT
ejpam-6387	159	34	]	]	PUNCT
ejpam-6387	159	35	du	du	PROPN
ejpam-6387	159	36	=	=	SYM
ejpam-6387	159	37	(	(	PUNCT
ejpam-6387	159	38	∫	∫	PROPN
ejpam-6387	159	39	a	a	DET
ejpam-6387	159	40	loga	loga	PROPN
ejpam-6387	159	41	+	+	CCONJ
ejpam-6387	159	42	∫	∫	PROPN
ejpam-6387	159	43	∞	∞	PROPN
ejpam-6387	159	44	a	a	DET
ejpam-6387	159	45	)	)	PUNCT
ejpam-6387	159	46	exp	exp	NOUN
ejpam-6387	159	47	[	[	PUNCT
ejpam-6387	159	48	−	−	PROPN
ejpam-6387	159	49	(	(	PUNCT
ejpam-6387	159	50	1	1	NUM
ejpam-6387	159	51	2	2	NUM
ejpam-6387	159	52	u+	u+	NOUN
ejpam-6387	159	53	logx	logx	NOUN
ejpam-6387	159	54	f(u	f(u	PROPN
ejpam-6387	159	55	)	)	PUNCT
ejpam-6387	159	56	)	)	PUNCT
ejpam-6387	159	57	]	]	PUNCT
ejpam-6387	159	58	du	du	VERB
ejpam-6387	159	59	for	for	ADP
ejpam-6387	159	60	some	some	DET
ejpam-6387	159	61	a	a	DET
ejpam-6387	159	62	>	>	X
ejpam-6387	159	63	log	log	PROPN
ejpam-6387	159	64	a.	a.	NOUN
ejpam-6387	159	65	where	where	SCONJ
ejpam-6387	159	66	the	the	DET
ejpam-6387	159	67	first	first	ADJ
ejpam-6387	159	68	integral	integral	ADJ
ejpam-6387	159	69	over	over	ADV
ejpam-6387	159	70	(	(	PUNCT
ejpam-6387	159	71	log	log	VERB
ejpam-6387	159	72	a	a	PRON
ejpam-6387	159	73	,	,	PUNCT
ejpam-6387	159	74	a	a	PRON
ejpam-6387	159	75	)	)	PUNCT
ejpam-6387	159	76	is∫	is∫	NOUN
ejpam-6387	159	77	a	a	DET
ejpam-6387	159	78	log	log	NOUN
ejpam-6387	159	79	a	a	DET
ejpam-6387	159	80	exp	exp	NOUN
ejpam-6387	159	81	[	[	PUNCT
ejpam-6387	159	82	−	−	PROPN
ejpam-6387	159	83	(	(	PUNCT
ejpam-6387	159	84	1	1	NUM
ejpam-6387	159	85	2	2	NUM
ejpam-6387	159	86	+	+	CCONJ
ejpam-6387	159	87	log	log	NOUN
ejpam-6387	159	88	x	x	SYM
ejpam-6387	159	89	f(u	f(u	PROPN
ejpam-6387	159	90	)	)	PUNCT
ejpam-6387	159	91	)	)	PUNCT
ejpam-6387	159	92	du	du	X
ejpam-6387	159	93	]	]	PUNCT
ejpam-6387	159	94	≤	≤	NUM
ejpam-6387	160	1	e	e	X
ejpam-6387	160	2	−	−	PROPN
ejpam-6387	160	3	log	log	NOUN
ejpam-6387	160	4	x	x	SYM
ejpam-6387	160	5	f(a	f(a	PROPN
ejpam-6387	160	6	)	)	PUNCT
ejpam-6387	160	7	∫	∫	PROPN
ejpam-6387	160	8	a	a	DET
ejpam-6387	160	9	log	log	NOUN
ejpam-6387	160	10	a	a	DET
ejpam-6387	160	11	e−	e−	PROPN
ejpam-6387	160	12	1	1	NUM
ejpam-6387	160	13	2	2	NUM
ejpam-6387	160	14	udu	udu	NOUN
ejpam-6387	160	15	=	=	SYM
ejpam-6387	160	16	o	o	NOUN
ejpam-6387	160	17	(	(	PUNCT
ejpam-6387	160	18	e	e	NOUN
ejpam-6387	160	19	−	−	PROPN
ejpam-6387	160	20	log	log	NOUN
ejpam-6387	160	21	x	x	SYM
ejpam-6387	160	22	f(a	f(a	NOUN
ejpam-6387	160	23	)	)	PUNCT
ejpam-6387	160	24	)	)	PUNCT
ejpam-6387	161	1	whilest	whilest	ADV
ejpam-6387	161	2	the	the	DET
ejpam-6387	161	3	second	second	ADJ
ejpam-6387	161	4	integeral	integeral	NOUN
ejpam-6387	161	5	over	over	ADP
ejpam-6387	161	6	the	the	DET
ejpam-6387	161	7	interval	interval	NOUN
ejpam-6387	161	8	(	(	PUNCT
ejpam-6387	161	9	a,∞	a,∞	PROPN
ejpam-6387	161	10	)	)	PUNCT
ejpam-6387	161	11	is,∫	is,∫	VERB
ejpam-6387	161	12	∞	∞	PROPN
ejpam-6387	161	13	a	a	DET
ejpam-6387	161	14	exp	exp	NOUN
ejpam-6387	161	15	[	[	PUNCT
ejpam-6387	161	16	−	−	PROPN
ejpam-6387	161	17	(	(	PUNCT
ejpam-6387	161	18	1	1	NUM
ejpam-6387	161	19	2	2	NUM
ejpam-6387	161	20	u+	u+	NOUN
ejpam-6387	161	21	logx	logx	NOUN
ejpam-6387	161	22	f(u	f(u	PROPN
ejpam-6387	161	23	)	)	PUNCT
ejpam-6387	161	24	)	)	PUNCT
ejpam-6387	162	1	du	du	PROPN
ejpam-6387	162	2	]	]	PUNCT
ejpam-6387	162	3	≤	≤	NUM
ejpam-6387	162	4	∫	∫	PROPN
ejpam-6387	162	5	∞	∞	PROPN
ejpam-6387	163	1	a	a	DET
ejpam-6387	163	2	e−	e−	PROPN
ejpam-6387	163	3	1	1	NUM
ejpam-6387	163	4	2	2	NUM
ejpam-6387	163	5	udu	udu	NOUN
ejpam-6387	163	6	=	=	NOUN
ejpam-6387	163	7	o	o	X
ejpam-6387	163	8	(	(	PUNCT
ejpam-6387	163	9	e−	e−	PROPN
ejpam-6387	163	10	1	1	NUM
ejpam-6387	163	11	2	2	NUM
ejpam-6387	163	12	a	a	PRON
ejpam-6387	163	13	)	)	PUNCT
ejpam-6387	163	14	using	use	VERB
ejpam-6387	163	15	the	the	DET
ejpam-6387	163	16	optimality	optimality	NOUN
ejpam-6387	163	17	for	for	ADP
ejpam-6387	163	18	the	the	DET
ejpam-6387	163	19	two	two	NUM
ejpam-6387	163	20	parts	part	NOUN
ejpam-6387	163	21	above	above	ADV
ejpam-6387	163	22	to	to	PART
ejpam-6387	163	23	get	get	VERB
ejpam-6387	163	24	:	:	PUNCT
ejpam-6387	163	25	o	o	X
ejpam-6387	163	26	(	(	PUNCT
ejpam-6387	163	27	e	e	X
ejpam-6387	163	28	−	−	PROPN
ejpam-6387	163	29	log	log	NOUN
ejpam-6387	163	30	x	x	SYM
ejpam-6387	163	31	f(a	f(a	NOUN
ejpam-6387	163	32	)	)	PUNCT
ejpam-6387	163	33	)	)	PUNCT
ejpam-6387	164	1	=	=	PUNCT
ejpam-6387	164	2	o	o	X
ejpam-6387	164	3	(	(	PUNCT
ejpam-6387	164	4	e−	e−	PROPN
ejpam-6387	164	5	1	1	NUM
ejpam-6387	164	6	2	2	NUM
ejpam-6387	164	7	a	a	NOUN
ejpam-6387	164	8	)	)	PUNCT
ejpam-6387	164	9	−	−	NOUN
ejpam-6387	164	10	log	log	NOUN
ejpam-6387	164	11	x	x	SYM
ejpam-6387	164	12	f(a	f(a	NOUN
ejpam-6387	164	13	)	)	PUNCT
ejpam-6387	164	14	=	=	SYM
ejpam-6387	164	15	−1	−1	NOUN
ejpam-6387	164	16	2	2	NUM
ejpam-6387	164	17	a	a	PRON
ejpam-6387	164	18	which	which	PRON
ejpam-6387	164	19	tells	tell	VERB
ejpam-6387	164	20	as	as	ADP
ejpam-6387	164	21	that	that	DET
ejpam-6387	164	22	h(a	h(a	PROPN
ejpam-6387	164	23	)	)	PUNCT
ejpam-6387	164	24	=	=	SYM
ejpam-6387	164	25	af(a	af(a	X
ejpam-6387	164	26	)	)	PUNCT
ejpam-6387	164	27	=	=	SYM
ejpam-6387	164	28	2	2	NUM
ejpam-6387	164	29	log	log	NOUN
ejpam-6387	164	30	x	x	PUNCT
ejpam-6387	164	31	which	which	PRON
ejpam-6387	164	32	means	mean	VERB
ejpam-6387	164	33	,	,	PUNCT
ejpam-6387	164	34	a	a	DET
ejpam-6387	164	35	=	=	X
ejpam-6387	164	36	h−1(2	h−1(2	PROPN
ejpam-6387	164	37	log	log	NOUN
ejpam-6387	164	38	x	x	NOUN
ejpam-6387	164	39	)	)	PUNCT
ejpam-6387	164	40	.	.	PUNCT
ejpam-6387	165	1	z.	z.	PROPN
ejpam-6387	165	2	m.	m.	PROPN
ejpam-6387	165	3	amen	amen	INTJ
ejpam-6387	165	4	,	,	PUNCT
ejpam-6387	165	5	f.	f.	PROPN
ejpam-6387	165	6	a.	a.	PROPN
ejpam-6387	165	7	al	al	PROPN
ejpam-6387	165	8	-	-	PUNCT
ejpam-6387	165	9	maamori	maamori	PROPN
ejpam-6387	165	10	,	,	PUNCT
ejpam-6387	165	11	m.	m.	NOUN
ejpam-6387	165	12	f.	f.	PROPN
ejpam-6387	165	13	hama	hama	PROPN
ejpam-6387	165	14	/	/	SYM
ejpam-6387	165	15	eur	eur	PROPN
ejpam-6387	165	16	.	.	PUNCT
ejpam-6387	166	1	j.	j.	PROPN
ejpam-6387	166	2	pure	pure	PROPN
ejpam-6387	166	3	appl	appl	PROPN
ejpam-6387	166	4	.	.	PROPN
ejpam-6387	166	5	math	math	PROPN
ejpam-6387	166	6	,	,	PUNCT
ejpam-6387	166	7	18	18	NUM
ejpam-6387	166	8	(	(	PUNCT
ejpam-6387	166	9	4	4	NUM
ejpam-6387	166	10	)	)	PUNCT
ejpam-6387	166	11	(	(	PUNCT
ejpam-6387	166	12	2025	2025	NUM
ejpam-6387	166	13	)	)	PUNCT
ejpam-6387	166	14	,	,	PUNCT
ejpam-6387	166	15	6387	6387	NUM
ejpam-6387	166	16	9	9	NUM
ejpam-6387	166	17	of	of	ADP
ejpam-6387	166	18	15	15	NUM
ejpam-6387	166	19	hence	hence	ADV
ejpam-6387	166	20	,	,	PUNCT
ejpam-6387	166	21	∣∣∣∣zp(x)−	∣∣∣∣zp(x)−	PROPN
ejpam-6387	166	22	β	β	X
ejpam-6387	166	23	2	2	NUM
ejpam-6387	166	24	x2	x2	PROPN
ejpam-6387	166	25	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6387	167	1	=	=	NOUN
ejpam-6387	167	2	o	o	X
ejpam-6387	167	3	(	(	PUNCT
ejpam-6387	167	4	x2exp	x2exp	PROPN
ejpam-6387	167	5	[	[	PUNCT
ejpam-6387	167	6	−1	−1	NOUN
ejpam-6387	167	7	2	2	NUM
ejpam-6387	167	8	h−1(2	h−1(2	NOUN
ejpam-6387	167	9	log	log	NOUN
ejpam-6387	167	10	x	x	NOUN
ejpam-6387	167	11	)	)	PUNCT
ejpam-6387	167	12	]	]	PUNCT
ejpam-6387	167	13	)	)	PUNCT
ejpam-6387	167	14	(	(	PUNCT
ejpam-6387	167	15	3	3	X
ejpam-6387	167	16	)	)	PUNCT
ejpam-6387	167	17	we	we	PRON
ejpam-6387	167	18	know	know	VERB
ejpam-6387	167	19	from	from	ADP
ejpam-6387	167	20	given	give	VERB
ejpam-6387	167	21	that	that	SCONJ
ejpam-6387	167	22	the	the	DET
ejpam-6387	167	23	function	function	NOUN
ejpam-6387	167	24	np	np	INTJ
ejpam-6387	167	25	is	be	AUX
ejpam-6387	167	26	increasing	increase	VERB
ejpam-6387	167	27	function	function	NOUN
ejpam-6387	167	28	,	,	PUNCT
ejpam-6387	167	29	so	so	CCONJ
ejpam-6387	167	30	for	for	ADP
ejpam-6387	167	31	every	every	PRON
ejpam-6387	167	32	0	0	NUM
ejpam-6387	167	33	<	<	X
ejpam-6387	167	34	y	y	X
ejpam-6387	167	35	<	<	X
ejpam-6387	167	36	x	x	X
ejpam-6387	167	37	,	,	PUNCT
ejpam-6387	167	38	we	we	PRON
ejpam-6387	167	39	have	have	VERB
ejpam-6387	167	40	∫	∫	PROPN
ejpam-6387	167	41	x	x	SYM
ejpam-6387	167	42	0	0	NUM
ejpam-6387	168	1	np(u)du−	np(u)du−	PROPN
ejpam-6387	168	2	∫	∫	PROPN
ejpam-6387	168	3	x−y	x−y	PROPN
ejpam-6387	168	4	0	0	NUM
ejpam-6387	169	1	np(u)du	np(u)du	PROPN
ejpam-6387	169	2	=	=	SYM
ejpam-6387	169	3	∫	∫	PROPN
ejpam-6387	170	1	x	x	X
ejpam-6387	171	1	x−y	x−y	PROPN
ejpam-6387	171	2	np(u)du	np(u)du	PROPN
ejpam-6387	171	3	≤	≤	PROPN
ejpam-6387	171	4	ynp(x	ynp(x	PROPN
ejpam-6387	171	5	)	)	PUNCT
ejpam-6387	171	6	on	on	ADP
ejpam-6387	171	7	the	the	DET
ejpam-6387	171	8	other	other	ADJ
ejpam-6387	171	9	hand,∫	hand,∫	PROPN
ejpam-6387	171	10	x+y	x+y	PROPN
ejpam-6387	171	11	0	0	NUM
ejpam-6387	172	1	np(u)du−	np(u)du−	NUM
ejpam-6387	172	2	∫	∫	PROPN
ejpam-6387	172	3	x	x	SYM
ejpam-6387	172	4	0	0	NUM
ejpam-6387	172	5	np(u)du	np(u)du	PROPN
ejpam-6387	172	6	=	=	SYM
ejpam-6387	172	7	∫	∫	PROPN
ejpam-6387	172	8	x+y	x+y	PROPN
ejpam-6387	172	9	x	x	PRON
ejpam-6387	172	10	np(u)du	np(u)du	PROPN
ejpam-6387	172	11	≥	≥	NUM
ejpam-6387	172	12	ynp(x	ynp(x	PROPN
ejpam-6387	172	13	)	)	PUNCT
ejpam-6387	172	14	.	.	PUNCT
ejpam-6387	173	1	therefore	therefore	ADV
ejpam-6387	173	2	,	,	PUNCT
ejpam-6387	173	3	zp(x)−zp(x−	zp(x)−zp(x−	PROPN
ejpam-6387	173	4	y	y	NOUN
ejpam-6387	173	5	)	)	PUNCT
ejpam-6387	173	6	y	y	PROPN
ejpam-6387	173	7	≤	≤	NOUN
ejpam-6387	173	8	np(x	np(x	NOUN
ejpam-6387	173	9	)	)	PUNCT
ejpam-6387	173	10	≤	≤	NOUN
ejpam-6387	173	11	zp(x+	zp(x+	NUM
ejpam-6387	173	12	y)−zp(x	y)−zp(x	PROPN
ejpam-6387	173	13	)	)	PUNCT
ejpam-6387	174	1	y	y	PROPN
ejpam-6387	174	2	using	use	VERB
ejpam-6387	174	3	equation	equation	NOUN
ejpam-6387	174	4	(	(	PUNCT
ejpam-6387	174	5	3	3	X
ejpam-6387	174	6	)	)	PUNCT
ejpam-6387	174	7	the	the	DET
ejpam-6387	174	8	left	left	ADJ
ejpam-6387	174	9	hand	hand	NOUN
ejpam-6387	174	10	side	side	NOUN
ejpam-6387	174	11	of	of	ADP
ejpam-6387	174	12	the	the	DET
ejpam-6387	174	13	above	above	ADJ
ejpam-6387	174	14	inequality	inequality	NOUN
ejpam-6387	174	15	is	be	AUX
ejpam-6387	174	16	=	=	SYM
ejpam-6387	174	17	1	1	NUM
ejpam-6387	174	18	y	y	PROPN
ejpam-6387	174	19	(	(	PUNCT
ejpam-6387	174	20	β	β	X
ejpam-6387	174	21	2	2	NUM
ejpam-6387	174	22	(	(	PUNCT
ejpam-6387	174	23	x2	x2	INTJ
ejpam-6387	174	24	−	−	PROPN
ejpam-6387	174	25	(	(	PUNCT
ejpam-6387	174	26	x−	x−	PROPN
ejpam-6387	174	27	y)2	y)2	NOUN
ejpam-6387	174	28	)	)	PUNCT
ejpam-6387	174	29	)	)	PUNCT
ejpam-6387	175	1	+	+	ADP
ejpam-6387	175	2	o	o	X
ejpam-6387	175	3	(	(	PUNCT
ejpam-6387	175	4	x2	x2	NOUN
ejpam-6387	175	5	exp	exp	PROPN
ejpam-6387	175	6	[	[	PUNCT
ejpam-6387	175	7	−1	−1	NOUN
ejpam-6387	175	8	2	2	NUM
ejpam-6387	175	9	h−1(2	h−1(2	PROPN
ejpam-6387	175	10	log(x−	log(x−	PUNCT
ejpam-6387	175	11	y	y	PROPN
ejpam-6387	175	12	)	)	PUNCT
ejpam-6387	175	13	)	)	PUNCT
ejpam-6387	176	1	]	]	PUNCT
ejpam-6387	176	2	)	)	PUNCT
ejpam-6387	176	3	.	.	PUNCT
ejpam-6387	177	1	that	that	PRON
ejpam-6387	177	2	is	be	AUX
ejpam-6387	177	3	the	the	DET
ejpam-6387	177	4	left	left	ADJ
ejpam-6387	177	5	hand	hand	NOUN
ejpam-6387	177	6	side	side	NOUN
ejpam-6387	177	7	is	be	AUX
ejpam-6387	177	8	,	,	PUNCT
ejpam-6387	177	9	=	=	PUNCT
ejpam-6387	177	10	1	1	NUM
ejpam-6387	177	11	y	y	PROPN
ejpam-6387	177	12	β	β	X
ejpam-6387	177	13	2	2	NUM
ejpam-6387	177	14	(	(	PUNCT
ejpam-6387	177	15	x2	x2	INTJ
ejpam-6387	177	16	−	−	PROPN
ejpam-6387	177	17	(	(	PUNCT
ejpam-6387	177	18	x2	x2	INTJ
ejpam-6387	178	1	−	−	PROPN
ejpam-6387	178	2	2xy	2xy	ADJ
ejpam-6387	178	3	+	+	CCONJ
ejpam-6387	178	4	y2	y2	NOUN
ejpam-6387	178	5	)	)	PUNCT
ejpam-6387	178	6	)	)	PUNCT
ejpam-6387	179	1	+	+	ADP
ejpam-6387	179	2	o	o	X
ejpam-6387	179	3	(	(	PUNCT
ejpam-6387	179	4	x2exp	x2exp	PROPN
ejpam-6387	179	5	[	[	PUNCT
ejpam-6387	179	6	−1	−1	NOUN
ejpam-6387	179	7	2	2	NUM
ejpam-6387	179	8	h−1(2	h−1(2	PROPN
ejpam-6387	179	9	log(x−	log(x−	PUNCT
ejpam-6387	179	10	y	y	PROPN
ejpam-6387	179	11	)	)	PUNCT
ejpam-6387	179	12	)	)	PUNCT
ejpam-6387	179	13	]	]	PUNCT
ejpam-6387	179	14	)	)	PUNCT
ejpam-6387	179	15	(	(	PUNCT
ejpam-6387	179	16	4	4	X
ejpam-6387	179	17	)	)	PUNCT
ejpam-6387	179	18	=	=	SYM
ejpam-6387	179	19	1	1	NUM
ejpam-6387	179	20	y	y	PROPN
ejpam-6387	179	21	(	(	PUNCT
ejpam-6387	179	22	βxy	βxy	PROPN
ejpam-6387	179	23	−	−	PROPN
ejpam-6387	179	24	βy2	βy2	NOUN
ejpam-6387	179	25	2	2	NUM
ejpam-6387	179	26	)	)	PUNCT
ejpam-6387	180	1	+	+	NOUN
ejpam-6387	180	2	o	o	X
ejpam-6387	180	3	(	(	PUNCT
ejpam-6387	180	4	x2	x2	NOUN
ejpam-6387	180	5	exp	exp	PROPN
ejpam-6387	180	6	[	[	PUNCT
ejpam-6387	180	7	−1	−1	NOUN
ejpam-6387	180	8	2	2	NUM
ejpam-6387	180	9	h−1(2	h−1(2	PROPN
ejpam-6387	180	10	log(x−	log(x−	PUNCT
ejpam-6387	180	11	y	y	PROPN
ejpam-6387	180	12	)	)	PUNCT
ejpam-6387	180	13	)	)	PUNCT
ejpam-6387	180	14	]	]	PUNCT
ejpam-6387	180	15	)	)	PUNCT
ejpam-6387	180	16	.	.	PUNCT
ejpam-6387	181	1	similarly	similarly	ADV
ejpam-6387	181	2	,	,	PUNCT
ejpam-6387	181	3	the	the	DET
ejpam-6387	181	4	right	right	ADJ
ejpam-6387	181	5	hand	hand	NOUN
ejpam-6387	181	6	side	side	NOUN
ejpam-6387	181	7	is	be	AUX
ejpam-6387	181	8	1	1	NUM
ejpam-6387	181	9	y	y	NOUN
ejpam-6387	181	10	(	(	PUNCT
ejpam-6387	181	11	βxy	βxy	PROPN
ejpam-6387	181	12	+	+	CCONJ
ejpam-6387	181	13	βy2	βy2	X
ejpam-6387	181	14	2	2	NUM
ejpam-6387	181	15	)	)	PUNCT
ejpam-6387	182	1	+	+	NOUN
ejpam-6387	182	2	o	o	X
ejpam-6387	182	3	(	(	PUNCT
ejpam-6387	182	4	x2	x2	NOUN
ejpam-6387	182	5	exp	exp	PROPN
ejpam-6387	182	6	[	[	PUNCT
ejpam-6387	182	7	−1	−1	NOUN
ejpam-6387	182	8	2	2	NUM
ejpam-6387	182	9	h−1(2	h−1(2	NOUN
ejpam-6387	182	10	log(x	log(x	NUM
ejpam-6387	182	11	)	)	PUNCT
ejpam-6387	182	12	)	)	PUNCT
ejpam-6387	182	13	]	]	PUNCT
ejpam-6387	182	14	)	)	PUNCT
ejpam-6387	182	15	now	now	ADV
ejpam-6387	182	16	for	for	ADP
ejpam-6387	182	17	some	some	DET
ejpam-6387	182	18	ε	ε	PROPN
ejpam-6387	182	19	>	>	X
ejpam-6387	182	20	0	0	PUNCT
ejpam-6387	183	1	and	and	CCONJ
ejpam-6387	184	1	d	d	X
ejpam-6387	184	2	>	>	X
ejpam-6387	184	3	0	0	NUM
ejpam-6387	184	4	we	we	PRON
ejpam-6387	184	5	have	have	VERB
ejpam-6387	184	6	,	,	PUNCT
ejpam-6387	184	7	h(x)−	h(x)−	PROPN
ejpam-6387	184	8	h(x−	h(x−	PROPN
ejpam-6387	184	9	d	d	PROPN
ejpam-6387	184	10	)	)	PUNCT
ejpam-6387	185	1	=	=	PUNCT
ejpam-6387	185	2	xf(x)−	xf(x)−	PROPN
ejpam-6387	185	3	(	(	PUNCT
ejpam-6387	185	4	x−	x−	PROPN
ejpam-6387	185	5	d)f(x−	d)f(x−	PROPN
ejpam-6387	185	6	d	d	PROPN
ejpam-6387	185	7	)	)	PUNCT
ejpam-6387	185	8	(	(	PUNCT
ejpam-6387	185	9	by	by	ADP
ejpam-6387	185	10	given	give	VERB
ejpam-6387	185	11	)	)	PUNCT
ejpam-6387	185	12	=	=	PUNCT
ejpam-6387	185	13	x(f(x)−	x(f(x)−	PUNCT
ejpam-6387	185	14	f(x−	f(x−	PROPN
ejpam-6387	185	15	d	d	NOUN
ejpam-6387	185	16	)	)	PUNCT
ejpam-6387	185	17	)	)	PUNCT
ejpam-6387	186	1	+	+	CCONJ
ejpam-6387	186	2	df(x−	df(x−	PROPN
ejpam-6387	186	3	d	d	NOUN
ejpam-6387	186	4	)	)	PUNCT
ejpam-6387	186	5	≥	≥	X
ejpam-6387	186	6	ε	ε	PROPN
ejpam-6387	186	7	>	>	PUNCT
ejpam-6387	186	8	0	0	PUNCT
ejpam-6387	187	1	this	this	PRON
ejpam-6387	187	2	means	mean	VERB
ejpam-6387	187	3	that	that	SCONJ
ejpam-6387	187	4	h(x)−	h(x)−	PROPN
ejpam-6387	187	5	ε	ε	PROPN
ejpam-6387	187	6	≥	≥	NUM
ejpam-6387	187	7	h(x−	h(x−	PROPN
ejpam-6387	187	8	d	d	PROPN
ejpam-6387	187	9	)	)	PUNCT
ejpam-6387	187	10	,	,	PUNCT
ejpam-6387	187	11	therefore	therefore	ADV
ejpam-6387	187	12	with	with	ADP
ejpam-6387	187	13	y	y	PROPN
ejpam-6387	187	14	=	=	SYM
ejpam-6387	187	15	o(x	o(x	PROPN
ejpam-6387	187	16	)	)	PUNCT
ejpam-6387	187	17	(	(	PUNCT
ejpam-6387	187	18	since	since	SCONJ
ejpam-6387	187	19	0	0	NUM
ejpam-6387	187	20	<	<	X
ejpam-6387	187	21	y	y	X
ejpam-6387	187	22	<	<	X
ejpam-6387	187	23	x	x	NOUN
ejpam-6387	187	24	)	)	PUNCT
ejpam-6387	187	25	h−1(2	h−1(2	PROPN
ejpam-6387	187	26	log(x−	log(x−	PROPN
ejpam-6387	187	27	y	y	PROPN
ejpam-6387	187	28	)	)	PUNCT
ejpam-6387	187	29	)	)	PUNCT
ejpam-6387	187	30	≥	≥	PROPN
ejpam-6387	187	31	h−1(2	h−1(2	PROPN
ejpam-6387	187	32	log(x−	log(x−	PUNCT
ejpam-6387	187	33	ε	ε	PROPN
ejpam-6387	187	34	)	)	PUNCT
ejpam-6387	187	35	)	)	PUNCT
ejpam-6387	187	36	≥	≥	PROPN
ejpam-6387	187	37	h−1(2	h−1(2	PROPN
ejpam-6387	187	38	log(x−	log(x−	NOUN
ejpam-6387	187	39	d	d	PROPN
ejpam-6387	187	40	)	)	PUNCT
ejpam-6387	187	41	)	)	PUNCT
ejpam-6387	187	42	so	so	ADV
ejpam-6387	187	43	replacing	replace	VERB
ejpam-6387	187	44	x−	x−	PROPN
ejpam-6387	187	45	y	y	PROPN
ejpam-6387	187	46	by	by	ADP
ejpam-6387	187	47	x	x	PROPN
ejpam-6387	187	48	of	of	ADP
ejpam-6387	187	49	equation	equation	NOUN
ejpam-6387	187	50	(	(	PUNCT
ejpam-6387	187	51	4	4	NUM
ejpam-6387	187	52	)	)	PUNCT
ejpam-6387	187	53	,	,	PUNCT
ejpam-6387	187	54	we	we	PRON
ejpam-6387	187	55	have	have	VERB
ejpam-6387	187	56	for	for	ADP
ejpam-6387	187	57	some	some	DET
ejpam-6387	187	58	m	m	NOUN
ejpam-6387	187	59	>	>	X
ejpam-6387	187	60	0	0	NUM
ejpam-6387	187	61	1	1	NUM
ejpam-6387	187	62	y	y	PROPN
ejpam-6387	187	63	(	(	PUNCT
ejpam-6387	187	64	βxy	βxy	PROPN
ejpam-6387	187	65	−	−	PROPN
ejpam-6387	187	66	βy2	βy2	NOUN
ejpam-6387	187	67	2	2	NUM
ejpam-6387	188	1	+	+	NOUN
ejpam-6387	188	2	m	m	VERB
ejpam-6387	188	3	(	(	PUNCT
ejpam-6387	188	4	x2	x2	NOUN
ejpam-6387	188	5	exp	exp	NOUN
ejpam-6387	188	6	[	[	PUNCT
ejpam-6387	188	7	−1	−1	NOUN
ejpam-6387	188	8	2	2	NUM
ejpam-6387	188	9	h−1(2	h−1(2	NOUN
ejpam-6387	188	10	log	log	NOUN
ejpam-6387	188	11	x	x	NOUN
ejpam-6387	188	12	)	)	PUNCT
ejpam-6387	188	13	]	]	PUNCT
ejpam-6387	188	14	)	)	PUNCT
ejpam-6387	188	15	)	)	PUNCT
ejpam-6387	189	1	(	(	PUNCT
ejpam-6387	189	2	5	5	X
ejpam-6387	189	3	)	)	PUNCT
ejpam-6387	189	4	z.	z.	PROPN
ejpam-6387	189	5	m.	m.	PROPN
ejpam-6387	189	6	amen	amen	PROPN
ejpam-6387	189	7	,	,	PUNCT
ejpam-6387	189	8	f.	f.	PROPN
ejpam-6387	189	9	a.	a.	PROPN
ejpam-6387	189	10	al	al	PROPN
ejpam-6387	189	11	-	-	PUNCT
ejpam-6387	189	12	maamori	maamori	PROPN
ejpam-6387	189	13	,	,	PUNCT
ejpam-6387	189	14	m.	m.	NOUN
ejpam-6387	189	15	f.	f.	PROPN
ejpam-6387	189	16	hama	hama	PROPN
ejpam-6387	189	17	/	/	SYM
ejpam-6387	189	18	eur	eur	PROPN
ejpam-6387	189	19	.	.	PUNCT
ejpam-6387	190	1	j.	j.	PROPN
ejpam-6387	190	2	pure	pure	PROPN
ejpam-6387	190	3	appl	appl	PROPN
ejpam-6387	190	4	.	.	PROPN
ejpam-6387	190	5	math	math	PROPN
ejpam-6387	190	6	,	,	PUNCT
ejpam-6387	190	7	18	18	NUM
ejpam-6387	190	8	(	(	PUNCT
ejpam-6387	190	9	4	4	NUM
ejpam-6387	190	10	)	)	PUNCT
ejpam-6387	190	11	(	(	PUNCT
ejpam-6387	190	12	2025	2025	NUM
ejpam-6387	190	13	)	)	PUNCT
ejpam-6387	190	14	,	,	PUNCT
ejpam-6387	190	15	6387	6387	NUM
ejpam-6387	190	16	10	10	NUM
ejpam-6387	190	17	of	of	ADP
ejpam-6387	190	18	15	15	NUM
ejpam-6387	190	19	assuming	assume	VERB
ejpam-6387	190	20	b	b	NOUN
ejpam-6387	190	21	=	=	SYM
ejpam-6387	190	22	−1	−1	NOUN
ejpam-6387	190	23	2h	2h	NUM
ejpam-6387	190	24	−1(2	−1(2	PROPN
ejpam-6387	190	25	log	log	PROPN
ejpam-6387	190	26	x	x	NOUN
ejpam-6387	190	27	)	)	PUNCT
ejpam-6387	190	28	,	,	PUNCT
ejpam-6387	190	29	so	so	SCONJ
ejpam-6387	190	30	formula	formula	NOUN
ejpam-6387	190	31	(	(	PUNCT
ejpam-6387	190	32	5	5	NUM
ejpam-6387	190	33	)	)	PUNCT
ejpam-6387	190	34	appears	appear	VERB
ejpam-6387	190	35	as	as	ADP
ejpam-6387	190	36	:	:	PUNCT
ejpam-6387	190	37	1	1	NUM
ejpam-6387	190	38	y	y	PROPN
ejpam-6387	190	39	(	(	PUNCT
ejpam-6387	190	40	βxy	βxy	PROPN
ejpam-6387	190	41	−	−	PROPN
ejpam-6387	190	42	βy2	βy2	NOUN
ejpam-6387	190	43	2	2	NUM
ejpam-6387	191	1	+	+	NOUN
ejpam-6387	191	2	m	m	PROPN
ejpam-6387	191	3	(	(	PUNCT
ejpam-6387	191	4	x2e	x2e	NOUN
ejpam-6387	191	5	b	b	NUM
ejpam-6387	191	6	2	2	NUM
ejpam-6387	191	7	)	)	PUNCT
ejpam-6387	191	8	)	)	PUNCT
ejpam-6387	191	9	take	take	VERB
ejpam-6387	191	10	y	y	NOUN
ejpam-6387	191	11	=	=	SYM
ejpam-6387	191	12	xe	xe	PROPN
ejpam-6387	191	13	b	b	PROPN
ejpam-6387	191	14	2	2	NUM
ejpam-6387	192	1	then	then	ADV
ejpam-6387	192	2	we	we	PRON
ejpam-6387	192	3	have	have	VERB
ejpam-6387	192	4	,	,	PUNCT
ejpam-6387	192	5	1	1	NUM
ejpam-6387	192	6	y	y	PROPN
ejpam-6387	192	7	(	(	PUNCT
ejpam-6387	192	8	βxy	βxy	PROPN
ejpam-6387	192	9	−	−	PROPN
ejpam-6387	192	10	βy2	βy2	NOUN
ejpam-6387	192	11	2	2	NUM
ejpam-6387	192	12	+	+	NOUN
ejpam-6387	192	13	my2	my2	NOUN
ejpam-6387	192	14	)	)	PUNCT
ejpam-6387	193	1	=	=	NOUN
ejpam-6387	194	1	βx−	βx−	PUNCT
ejpam-6387	194	2	βy	βy	PRON
ejpam-6387	194	3	2	2	NUM
ejpam-6387	195	1	+	+	NOUN
ejpam-6387	195	2	my	my	PRON
ejpam-6387	195	3	=	=	ADJ
ejpam-6387	195	4	βx+	βx+	NOUN
ejpam-6387	195	5	y	y	PROPN
ejpam-6387	196	1	(	(	PUNCT
ejpam-6387	196	2	m−	m−	PROPN
ejpam-6387	196	3	y	y	PROPN
ejpam-6387	196	4	2	2	NUM
ejpam-6387	196	5	)	)	PUNCT
ejpam-6387	196	6	=	=	SYM
ejpam-6387	196	7	βx+o(y	βx+o(y	PROPN
ejpam-6387	196	8	)	)	PUNCT
ejpam-6387	196	9	hence	hence	ADV
ejpam-6387	196	10	,	,	PUNCT
ejpam-6387	196	11	np(x	np(x	NUM
ejpam-6387	196	12	)	)	PUNCT
ejpam-6387	196	13	=	=	SYM
ejpam-6387	196	14	βx+o(y	βx+o(y	PROPN
ejpam-6387	196	15	)	)	PUNCT
ejpam-6387	196	16	where	where	SCONJ
ejpam-6387	196	17	y	y	NOUN
ejpam-6387	196	18	=	=	PUNCT
ejpam-6387	196	19	x	x	SYM
ejpam-6387	196	20	exp	exp	NOUN
ejpam-6387	196	21	(	(	PUNCT
ejpam-6387	196	22	−1	−1	NOUN
ejpam-6387	196	23	4h	4h	PROPN
ejpam-6387	196	24	−1(2	−1(2	PROPN
ejpam-6387	196	25	log	log	PROPN
ejpam-6387	196	26	x	x	NOUN
ejpam-6387	196	27	)	)	PUNCT
ejpam-6387	196	28	)	)	PUNCT
ejpam-6387	196	29	np(x	np(x	X
ejpam-6387	196	30	)	)	PUNCT
ejpam-6387	196	31	=	=	SYM
ejpam-6387	196	32	βx+o	βx+o	PROPN
ejpam-6387	196	33	(	(	PUNCT
ejpam-6387	196	34	x	x	SYM
ejpam-6387	196	35	exp	exp	NOUN
ejpam-6387	196	36	(	(	PUNCT
ejpam-6387	196	37	−1	−1	NOUN
ejpam-6387	196	38	4	4	NUM
ejpam-6387	196	39	h−1(2	h−1(2	NOUN
ejpam-6387	196	40	log	log	NOUN
ejpam-6387	196	41	x	x	NOUN
ejpam-6387	196	42	)	)	PUNCT
ejpam-6387	196	43	)	)	PUNCT
ejpam-6387	196	44	)	)	PUNCT
ejpam-6387	196	45	.	.	PUNCT
ejpam-6387	197	1	the	the	DET
ejpam-6387	197	2	above	above	ADJ
ejpam-6387	197	3	work	work	NOUN
ejpam-6387	197	4	shows	show	VERB
ejpam-6387	197	5	that	that	SCONJ
ejpam-6387	197	6	”	"	PUNCT
ejpam-6387	197	7	how	how	SCONJ
ejpam-6387	197	8	the	the	DET
ejpam-6387	197	9	size	size	NOUN
ejpam-6387	197	10	of	of	ADP
ejpam-6387	197	11	error	error	NOUN
ejpam-6387	197	12	term	term	NOUN
ejpam-6387	197	13	of	of	ADP
ejpam-6387	197	14	np(x	np(x	NOUN
ejpam-6387	197	15	)	)	PUNCT
ejpam-6387	197	16	affected	affect	VERB
ejpam-6387	197	17	by	by	ADP
ejpam-6387	197	18	changing	change	VERB
ejpam-6387	197	19	the	the	DET
ejpam-6387	197	20	size	size	NOUN
ejpam-6387	197	21	of	of	ADP
ejpam-6387	197	22	error	error	NOUN
ejpam-6387	197	23	term	term	NOUN
ejpam-6387	197	24	of	of	ADP
ejpam-6387	197	25	ζp(s	ζp(s	NOUN
ejpam-6387	197	26	)	)	PUNCT
ejpam-6387	197	27	”	"	PUNCT
ejpam-6387	197	28	.	.	PUNCT
ejpam-6387	198	1	therefore	therefore	ADV
ejpam-6387	198	2	,	,	PUNCT
ejpam-6387	198	3	by	by	ADP
ejpam-6387	198	4	using	use	VERB
ejpam-6387	198	5	the	the	DET
ejpam-6387	198	6	same	same	ADJ
ejpam-6387	198	7	strategies	strategy	NOUN
ejpam-6387	198	8	by	by	ADP
ejpam-6387	198	9	repeating	repeat	VERB
ejpam-6387	198	10	the	the	DET
ejpam-6387	198	11	above	above	ADJ
ejpam-6387	198	12	proof	proof	NOUN
ejpam-6387	198	13	,	,	PUNCT
ejpam-6387	198	14	observing	observe	VERB
ejpam-6387	198	15	the	the	DET
ejpam-6387	198	16	following	follow	VERB
ejpam-6387	198	17	table	table	NOUN
ejpam-6387	198	18	:	:	PUNCT
ejpam-6387	198	19	table	table	NOUN
ejpam-6387	198	20	1	1	NUM
ejpam-6387	198	21	:	:	PUNCT
ejpam-6387	198	22	size	size	NOUN
ejpam-6387	198	23	of	of	ADP
ejpam-6387	198	24	error	error	NOUN
ejpam-6387	198	25	term	term	NOUN
ejpam-6387	198	26	of	of	ADP
ejpam-6387	198	27	np(x	np(x	NOUN
ejpam-6387	198	28	)	)	PUNCT
ejpam-6387	198	29	affected	affect	VERB
ejpam-6387	198	30	by	by	ADP
ejpam-6387	198	31	c	c	PROPN
ejpam-6387	198	32	between	between	ADP
ejpam-6387	198	33	(	(	PUNCT
ejpam-6387	198	34	0	0	NUM
ejpam-6387	198	35	,	,	PUNCT
ejpam-6387	198	36	1	1	NUM
ejpam-6387	198	37	)	)	PUNCT
ejpam-6387	198	38	ζp(s	ζp(s	NUM
ejpam-6387	198	39	)	)	PUNCT
ejpam-6387	198	40	np(x	np(x	NUM
ejpam-6387	198	41	)	)	PUNCT
ejpam-6387	198	42	o(t0.1	o(t0.1	NOUN
ejpam-6387	198	43	)	)	PUNCT
ejpam-6387	198	44	βx+o	βx+o	PROPN
ejpam-6387	198	45	(	(	PUNCT
ejpam-6387	198	46	x	x	SYM
ejpam-6387	198	47	exp	exp	NOUN
ejpam-6387	198	48	(	(	PUNCT
ejpam-6387	198	49	−	−	PROPN
ejpam-6387	198	50	9	9	NUM
ejpam-6387	198	51	20h	20h	NOUN
ejpam-6387	198	52	−1(109	−1(109	VERB
ejpam-6387	198	53	log	log	PROPN
ejpam-6387	198	54	x	x	NOUN
ejpam-6387	198	55	)	)	PUNCT
ejpam-6387	198	56	)	)	PUNCT
ejpam-6387	198	57	)	)	PUNCT
ejpam-6387	199	1	o(t0.5	o(t0.5	PROPN
ejpam-6387	199	2	)	)	PUNCT
ejpam-6387	199	3	βx+o	βx+o	NUM
ejpam-6387	199	4	(	(	PUNCT
ejpam-6387	199	5	x	x	SYM
ejpam-6387	199	6	exp	exp	NOUN
ejpam-6387	199	7	(	(	PUNCT
ejpam-6387	199	8	−1	−1	NOUN
ejpam-6387	199	9	4h	4h	PROPN
ejpam-6387	199	10	−1(2	−1(2	PROPN
ejpam-6387	199	11	log	log	PROPN
ejpam-6387	199	12	x	x	NOUN
ejpam-6387	199	13	)	)	PUNCT
ejpam-6387	199	14	)	)	PUNCT
ejpam-6387	199	15	)	)	PUNCT
ejpam-6387	199	16	o(t0.9	o(t0.9	NOUN
ejpam-6387	199	17	)	)	PUNCT
ejpam-6387	199	18	βx+o	βx+o	PUNCT
ejpam-6387	199	19	(	(	PUNCT
ejpam-6387	199	20	x	x	SYM
ejpam-6387	199	21	exp	exp	NOUN
ejpam-6387	199	22	(	(	PUNCT
ejpam-6387	199	23	−	−	PROPN
ejpam-6387	199	24	1	1	NUM
ejpam-6387	199	25	20h	20h	NUM
ejpam-6387	199	26	−1(10logx	−1(10logx	PROPN
ejpam-6387	199	27	)	)	PUNCT
ejpam-6387	199	28	)	)	PUNCT
ejpam-6387	199	29	)	)	PUNCT
ejpam-6387	199	30	from	from	ADP
ejpam-6387	199	31	the	the	DET
ejpam-6387	199	32	above	above	ADJ
ejpam-6387	199	33	table	table	NOUN
ejpam-6387	199	34	,	,	PUNCT
ejpam-6387	199	35	one	one	PRON
ejpam-6387	199	36	can	can	AUX
ejpam-6387	199	37	see	see	VERB
ejpam-6387	199	38	that	that	SCONJ
ejpam-6387	199	39	the	the	DET
ejpam-6387	199	40	error	error	NOUN
ejpam-6387	199	41	terms	term	NOUN
ejpam-6387	199	42	of	of	ADP
ejpam-6387	199	43	np(x	np(x	NOUN
ejpam-6387	199	44	)	)	PUNCT
ejpam-6387	199	45	is	be	AUX
ejpam-6387	199	46	always	always	ADV
ejpam-6387	199	47	negative	negative	ADJ
ejpam-6387	199	48	when	when	SCONJ
ejpam-6387	199	49	0	0	NUM
ejpam-6387	199	50	<	<	X
ejpam-6387	199	51	c	c	X
ejpam-6387	199	52	<	<	X
ejpam-6387	199	53	1	1	NUM
ejpam-6387	199	54	and	and	CCONJ
ejpam-6387	199	55	get	get	VERB
ejpam-6387	199	56	smaller	small	ADJ
ejpam-6387	199	57	as	as	SCONJ
ejpam-6387	199	58	c	c	NOUN
ejpam-6387	199	59	get	get	VERB
ejpam-6387	199	60	closer	close	ADJ
ejpam-6387	199	61	to	to	ADP
ejpam-6387	199	62	0	0	NUM
ejpam-6387	199	63	and	and	CCONJ
ejpam-6387	199	64	it	it	PRON
ejpam-6387	199	65	gets	get	VERB
ejpam-6387	199	66	bigger	big	ADJ
ejpam-6387	199	67	as	as	ADP
ejpam-6387	199	68	c	c	NOUN
ejpam-6387	199	69	closer	close	ADV
ejpam-6387	199	70	to	to	ADP
ejpam-6387	199	71	1	1	NUM
ejpam-6387	199	72	.	.	PUNCT
ejpam-6387	200	1	now	now	ADV
ejpam-6387	200	2	the	the	DET
ejpam-6387	200	3	interseting	interseting	ADJ
ejpam-6387	200	4	point	point	NOUN
ejpam-6387	200	5	is	be	AUX
ejpam-6387	200	6	that	that	SCONJ
ejpam-6387	200	7	what	what	PRON
ejpam-6387	200	8	will	will	AUX
ejpam-6387	200	9	happen	happen	VERB
ejpam-6387	200	10	to	to	ADP
ejpam-6387	200	11	the	the	DET
ejpam-6387	200	12	size	size	NOUN
ejpam-6387	200	13	of	of	ADP
ejpam-6387	200	14	error	error	NOUN
ejpam-6387	200	15	term	term	NOUN
ejpam-6387	200	16	of	of	ADP
ejpam-6387	200	17	np(x	np(x	NOUN
ejpam-6387	200	18	)	)	PUNCT
ejpam-6387	200	19	when	when	SCONJ
ejpam-6387	200	20	c	c	X
ejpam-6387	200	21	>	>	X
ejpam-6387	200	22	1	1	X
ejpam-6387	200	23	.	.	PUNCT
ejpam-6387	201	1	first	first	ADV
ejpam-6387	201	2	,	,	PUNCT
ejpam-6387	201	3	we	we	PRON
ejpam-6387	201	4	will	will	AUX
ejpam-6387	201	5	find	find	VERB
ejpam-6387	201	6	the	the	DET
ejpam-6387	201	7	error	error	NOUN
ejpam-6387	201	8	term	term	NOUN
ejpam-6387	201	9	of	of	ADP
ejpam-6387	201	10	np(x	np(x	NOUN
ejpam-6387	201	11	)	)	PUNCT
ejpam-6387	201	12	when	when	SCONJ
ejpam-6387	201	13	c	c	NOUN
ejpam-6387	201	14	=	=	SYM
ejpam-6387	201	15	3	3	NUM
ejpam-6387	201	16	2	2	NUM
ejpam-6387	201	17	.	.	PUNCT
ejpam-6387	202	1	the	the	DET
ejpam-6387	202	2	proof	proof	NOUN
ejpam-6387	202	3	has	have	VERB
ejpam-6387	202	4	the	the	DET
ejpam-6387	202	5	same	same	ADJ
ejpam-6387	202	6	step	step	NOUN
ejpam-6387	202	7	untill	untill	NOUN
ejpam-6387	202	8	we	we	PRON
ejpam-6387	202	9	get	get	VERB
ejpam-6387	202	10	to	to	ADP
ejpam-6387	202	11	the	the	DET
ejpam-6387	202	12	following	follow	VERB
ejpam-6387	202	13	step	step	NOUN
ejpam-6387	202	14	:	:	PUNCT
ejpam-6387	202	15	∣∣∣∣zp(x)−	∣∣∣∣zp(x)−	PROPN
ejpam-6387	202	16	β	β	X
ejpam-6387	202	17	2	2	NUM
ejpam-6387	202	18	x2	x2	PROPN
ejpam-6387	202	19	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6387	203	1	=	=	NOUN
ejpam-6387	203	2	o	o	PROPN
ejpam-6387	203	3	(	(	PUNCT
ejpam-6387	203	4	x2	x2	NOUN
ejpam-6387	203	5	∫	∫	PROPN
ejpam-6387	204	1	∞	∞	PROPN
ejpam-6387	204	2	log	log	VERB
ejpam-6387	204	3	a	a	DET
ejpam-6387	204	4	exp	exp	NOUN
ejpam-6387	204	5	[	[	PUNCT
ejpam-6387	204	6	−	−	PROPN
ejpam-6387	204	7	(	(	PUNCT
ejpam-6387	204	8	(	(	PUNCT
ejpam-6387	204	9	1−	1−	NUM
ejpam-6387	204	10	c)u+	c)u+	PROPN
ejpam-6387	204	11	log	log	VERB
ejpam-6387	204	12	x	x	PUNCT
ejpam-6387	204	13	f(u	f(u	PROPN
ejpam-6387	204	14	)	)	PUNCT
ejpam-6387	204	15	)	)	PUNCT
ejpam-6387	204	16	]	]	PUNCT
ejpam-6387	205	1	du	du	X
ejpam-6387	205	2	)	)	PUNCT
ejpam-6387	206	1	+	+	ADP
ejpam-6387	206	2	o	o	X
ejpam-6387	206	3	(	(	PUNCT
ejpam-6387	206	4	x	x	SYM
ejpam-6387	206	5	2−	2−	NUM
ejpam-6387	206	6	1	1	NUM
ejpam-6387	206	7	f(log	f(log	PROPN
ejpam-6387	206	8	a	a	NOUN
ejpam-6387	206	9	)	)	PUNCT
ejpam-6387	206	10	)	)	PUNCT
ejpam-6387	206	11	since	since	SCONJ
ejpam-6387	206	12	c	c	NOUN
ejpam-6387	206	13	=	=	SYM
ejpam-6387	206	14	3	3	NUM
ejpam-6387	206	15	2	2	NUM
ejpam-6387	206	16	,	,	PUNCT
ejpam-6387	206	17	then	then	ADV
ejpam-6387	206	18	1−	1−	NUM
ejpam-6387	206	19	c	c	NOUN
ejpam-6387	206	20	=	=	SYM
ejpam-6387	206	21	−1	−1	NOUN
ejpam-6387	206	22	2	2	NUM
ejpam-6387	206	23	,	,	PUNCT
ejpam-6387	206	24	so	so	CCONJ
ejpam-6387	206	25	the	the	DET
ejpam-6387	206	26	above	above	ADJ
ejpam-6387	206	27	equation	equation	NOUN
ejpam-6387	206	28	becomes	become	VERB
ejpam-6387	206	29	∣∣∣∣zp(x)−	∣∣∣∣zp(x)−	PROPN
ejpam-6387	206	30	β	β	X
ejpam-6387	206	31	2	2	NUM
ejpam-6387	206	32	x2	x2	NOUN
ejpam-6387	206	33	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6387	207	1	=	=	NOUN
ejpam-6387	207	2	o	o	PROPN
ejpam-6387	207	3	(	(	PUNCT
ejpam-6387	207	4	x2	x2	NOUN
ejpam-6387	207	5	∫	∫	PROPN
ejpam-6387	208	1	∞	∞	PROPN
ejpam-6387	208	2	log	log	VERB
ejpam-6387	208	3	a	a	DET
ejpam-6387	208	4	exp	exp	NOUN
ejpam-6387	208	5	[	[	PUNCT
ejpam-6387	208	6	−	−	PROPN
ejpam-6387	208	7	(	(	PUNCT
ejpam-6387	208	8	−1	−1	NOUN
ejpam-6387	208	9	2	2	NUM
ejpam-6387	208	10	u+	u+	NOUN
ejpam-6387	208	11	log	log	NOUN
ejpam-6387	208	12	x	x	NOUN
ejpam-6387	208	13	f(u	f(u	PROPN
ejpam-6387	208	14	)	)	PUNCT
ejpam-6387	208	15	)	)	PUNCT
ejpam-6387	208	16	]	]	PUNCT
ejpam-6387	209	1	du	du	X
ejpam-6387	209	2	)	)	PUNCT
ejpam-6387	210	1	+	+	ADP
ejpam-6387	210	2	o	o	X
ejpam-6387	210	3	(	(	PUNCT
ejpam-6387	210	4	x	x	SYM
ejpam-6387	210	5	2−	2−	NUM
ejpam-6387	210	6	1	1	NUM
ejpam-6387	210	7	f(log	f(log	PROPN
ejpam-6387	210	8	a	a	NOUN
ejpam-6387	210	9	)	)	PUNCT
ejpam-6387	210	10	)	)	PUNCT
ejpam-6387	210	11	z.	z.	PROPN
ejpam-6387	210	12	m.	m.	PROPN
ejpam-6387	210	13	amen	amen	INTJ
ejpam-6387	210	14	,	,	PUNCT
ejpam-6387	210	15	f.	f.	PROPN
ejpam-6387	210	16	a.	a.	PROPN
ejpam-6387	210	17	al	al	PROPN
ejpam-6387	210	18	-	-	PUNCT
ejpam-6387	210	19	maamori	maamori	PROPN
ejpam-6387	210	20	,	,	PUNCT
ejpam-6387	210	21	m.	m.	NOUN
ejpam-6387	210	22	f.	f.	PROPN
ejpam-6387	210	23	hama	hama	PROPN
ejpam-6387	210	24	/	/	SYM
ejpam-6387	210	25	eur	eur	PROPN
ejpam-6387	210	26	.	.	PUNCT
ejpam-6387	211	1	j.	j.	PROPN
ejpam-6387	211	2	pure	pure	PROPN
ejpam-6387	211	3	appl	appl	PROPN
ejpam-6387	211	4	.	.	PROPN
ejpam-6387	211	5	math	math	PROPN
ejpam-6387	211	6	,	,	PUNCT
ejpam-6387	211	7	18	18	NUM
ejpam-6387	211	8	(	(	PUNCT
ejpam-6387	211	9	4	4	NUM
ejpam-6387	211	10	)	)	PUNCT
ejpam-6387	211	11	(	(	PUNCT
ejpam-6387	211	12	2025	2025	NUM
ejpam-6387	211	13	)	)	PUNCT
ejpam-6387	211	14	,	,	PUNCT
ejpam-6387	211	15	6387	6387	NUM
ejpam-6387	211	16	11	11	NUM
ejpam-6387	211	17	of	of	ADP
ejpam-6387	211	18	15	15	NUM
ejpam-6387	211	19	after	after	ADP
ejpam-6387	211	20	doing	do	VERB
ejpam-6387	211	21	some	some	DET
ejpam-6387	211	22	manipulations	manipulation	NOUN
ejpam-6387	211	23	one	one	PRON
ejpam-6387	211	24	could	could	AUX
ejpam-6387	211	25	see	see	VERB
ejpam-6387	211	26	that	that	SCONJ
ejpam-6387	211	27	the	the	DET
ejpam-6387	211	28	first	first	ADJ
ejpam-6387	211	29	integral	integral	ADJ
ejpam-6387	211	30	over	over	ADV
ejpam-6387	211	31	(	(	PUNCT
ejpam-6387	211	32	log	log	VERB
ejpam-6387	211	33	a	a	DET
ejpam-6387	211	34	,	,	PUNCT
ejpam-6387	211	35	a	a	PRON
ejpam-6387	211	36	)	)	PUNCT
ejpam-6387	211	37	is	be	AUX
ejpam-6387	211	38	:	:	PUNCT
ejpam-6387	211	39	∫	∫	PROPN
ejpam-6387	211	40	a	a	DET
ejpam-6387	211	41	log	log	NOUN
ejpam-6387	211	42	a	a	DET
ejpam-6387	211	43	exp	exp	NOUN
ejpam-6387	211	44	[	[	PUNCT
ejpam-6387	211	45	−	−	PROPN
ejpam-6387	211	46	(	(	PUNCT
ejpam-6387	211	47	−1	−1	NOUN
ejpam-6387	211	48	2	2	NUM
ejpam-6387	211	49	u+	u+	NOUN
ejpam-6387	211	50	log	log	NOUN
ejpam-6387	211	51	x	x	NOUN
ejpam-6387	211	52	f(u	f(u	PROPN
ejpam-6387	211	53	)	)	PUNCT
ejpam-6387	211	54	)	)	PUNCT
ejpam-6387	211	55	]	]	PUNCT
ejpam-6387	212	1	du	du	PROPN
ejpam-6387	212	2	=	=	SYM
ejpam-6387	212	3	o	o	PROPN
ejpam-6387	212	4	(	(	PUNCT
ejpam-6387	212	5	e	e	NOUN
ejpam-6387	212	6	−	−	PROPN
ejpam-6387	212	7	log	log	NOUN
ejpam-6387	212	8	x	x	SYM
ejpam-6387	212	9	f(a	f(a	NOUN
ejpam-6387	212	10	)	)	PUNCT
ejpam-6387	212	11	)	)	PUNCT
ejpam-6387	212	12	.	.	PUNCT
ejpam-6387	213	1	∫	∫	PROPN
ejpam-6387	214	1	∞	∞	PROPN
ejpam-6387	215	1	a	a	DET
ejpam-6387	215	2	exp	exp	NOUN
ejpam-6387	215	3	[	[	PUNCT
ejpam-6387	215	4	−	−	PROPN
ejpam-6387	215	5	(	(	PUNCT
ejpam-6387	215	6	−1	−1	NOUN
ejpam-6387	215	7	2	2	NUM
ejpam-6387	215	8	u+	u+	NOUN
ejpam-6387	215	9	log	log	NOUN
ejpam-6387	215	10	x	x	NOUN
ejpam-6387	215	11	f(u	f(u	PROPN
ejpam-6387	215	12	)	)	PUNCT
ejpam-6387	215	13	)	)	PUNCT
ejpam-6387	215	14	]	]	PUNCT
ejpam-6387	216	1	du	du	PROPN
ejpam-6387	216	2	=	=	SYM
ejpam-6387	216	3	o	o	PROPN
ejpam-6387	216	4	(	(	PUNCT
ejpam-6387	216	5	e	e	NOUN
ejpam-6387	216	6	1	1	NUM
ejpam-6387	216	7	2	2	NUM
ejpam-6387	216	8	a	a	PRON
ejpam-6387	216	9	)	)	PUNCT
ejpam-6387	216	10	similarly	similarly	ADV
ejpam-6387	216	11	choosing	choose	VERB
ejpam-6387	216	12	a	a	DET
ejpam-6387	216	13	opitamally	opitamally	ADV
ejpam-6387	216	14	such	such	ADJ
ejpam-6387	216	15	that	that	SCONJ
ejpam-6387	216	16	o	o	NOUN
ejpam-6387	216	17	−	−	ADP
ejpam-6387	216	18	terms	term	NOUN
ejpam-6387	216	19	will	will	AUX
ejpam-6387	216	20	be	be	AUX
ejpam-6387	216	21	:	:	PUNCT
ejpam-6387	216	22	o	o	X
ejpam-6387	216	23	(	(	PUNCT
ejpam-6387	216	24	e	e	X
ejpam-6387	216	25	−	−	PROPN
ejpam-6387	216	26	log	log	NOUN
ejpam-6387	216	27	x	x	SYM
ejpam-6387	216	28	f(a	f(a	NOUN
ejpam-6387	216	29	)	)	PUNCT
ejpam-6387	216	30	)	)	PUNCT
ejpam-6387	217	1	=	=	PUNCT
ejpam-6387	217	2	o	o	NOUN
ejpam-6387	217	3	(	(	PUNCT
ejpam-6387	217	4	e	e	NOUN
ejpam-6387	217	5	1	1	NUM
ejpam-6387	217	6	2	2	NUM
ejpam-6387	217	7	a	a	NOUN
ejpam-6387	217	8	)	)	PUNCT
ejpam-6387	217	9	a	a	DET
ejpam-6387	217	10	=	=	SYM
ejpam-6387	217	11	h−1(−2	h−1(−2	PROPN
ejpam-6387	217	12	log	log	NOUN
ejpam-6387	217	13	x	x	NOUN
ejpam-6387	217	14	)	)	PUNCT
ejpam-6387	217	15	hence	hence	ADV
ejpam-6387	217	16	∫	∫	PROPN
ejpam-6387	218	1	∞	∞	PROPN
ejpam-6387	218	2	log	log	VERB
ejpam-6387	218	3	a	a	DET
ejpam-6387	218	4	exp	exp	NOUN
ejpam-6387	218	5	[	[	PUNCT
ejpam-6387	218	6	−	−	PROPN
ejpam-6387	218	7	(	(	PUNCT
ejpam-6387	218	8	−1	−1	NOUN
ejpam-6387	218	9	2	2	NUM
ejpam-6387	218	10	u+	u+	NOUN
ejpam-6387	218	11	log	log	NOUN
ejpam-6387	218	12	x	x	NOUN
ejpam-6387	218	13	f(u	f(u	PROPN
ejpam-6387	218	14	)	)	PUNCT
ejpam-6387	218	15	)	)	PUNCT
ejpam-6387	218	16	]	]	PUNCT
ejpam-6387	219	1	du	du	PROPN
ejpam-6387	219	2	=	=	SYM
ejpam-6387	219	3	o	o	PROPN
ejpam-6387	219	4	(	(	PUNCT
ejpam-6387	219	5	exp	exp	NOUN
ejpam-6387	219	6	(	(	PUNCT
ejpam-6387	219	7	1	1	NUM
ejpam-6387	219	8	2	2	NUM
ejpam-6387	219	9	h−1(−2	h−1(−2	NOUN
ejpam-6387	219	10	log	log	NOUN
ejpam-6387	219	11	x	x	NOUN
ejpam-6387	219	12	)	)	PUNCT
ejpam-6387	219	13	)	)	PUNCT
ejpam-6387	219	14	)	)	PUNCT
ejpam-6387	219	15	and	and	CCONJ
ejpam-6387	219	16	np(x	np(x	NUM
ejpam-6387	219	17	)	)	PUNCT
ejpam-6387	219	18	=	=	SYM
ejpam-6387	219	19	βx+o	βx+o	PROPN
ejpam-6387	219	20	(	(	PUNCT
ejpam-6387	219	21	x	x	SYM
ejpam-6387	219	22	exp	exp	X
ejpam-6387	219	23	(	(	PUNCT
ejpam-6387	219	24	1	1	NUM
ejpam-6387	219	25	4	4	NUM
ejpam-6387	219	26	h−1(−2	h−1(−2	NOUN
ejpam-6387	219	27	log	log	NOUN
ejpam-6387	219	28	x	x	NOUN
ejpam-6387	219	29	)	)	PUNCT
ejpam-6387	219	30	)	)	PUNCT
ejpam-6387	219	31	)	)	PUNCT
ejpam-6387	219	32	from	from	ADP
ejpam-6387	219	33	the	the	DET
ejpam-6387	219	34	above	above	ADJ
ejpam-6387	219	35	result	result	NOUN
ejpam-6387	219	36	,	,	PUNCT
ejpam-6387	219	37	one	one	PRON
ejpam-6387	219	38	can	can	AUX
ejpam-6387	219	39	see	see	VERB
ejpam-6387	219	40	that	that	SCONJ
ejpam-6387	219	41	the	the	DET
ejpam-6387	219	42	error	error	NOUN
ejpam-6387	219	43	term	term	NOUN
ejpam-6387	219	44	of	of	ADP
ejpam-6387	219	45	np(x	np(x	NOUN
ejpam-6387	219	46	)	)	PUNCT
ejpam-6387	219	47	where	where	SCONJ
ejpam-6387	219	48	1	1	NUM
ejpam-6387	219	49	<	<	X
ejpam-6387	219	50	c	c	X
ejpam-6387	219	51	<	<	X
ejpam-6387	219	52	2	2	NUM
ejpam-6387	219	53	is	be	AUX
ejpam-6387	219	54	positive	positive	ADJ
ejpam-6387	219	55	and	and	CCONJ
ejpam-6387	219	56	big	big	ADJ
ejpam-6387	219	57	.	.	PUNCT
ejpam-6387	220	1	its	its	PRON
ejpam-6387	220	2	remain	remain	VERB
ejpam-6387	220	3	here	here	ADV
ejpam-6387	220	4	to	to	PART
ejpam-6387	220	5	mention	mention	VERB
ejpam-6387	220	6	what	what	PRON
ejpam-6387	220	7	is	be	AUX
ejpam-6387	220	8	the	the	DET
ejpam-6387	220	9	effection	effection	NOUN
ejpam-6387	220	10	of	of	ADP
ejpam-6387	220	11	c	c	PROPN
ejpam-6387	220	12	=	=	SYM
ejpam-6387	220	13	1	1	NUM
ejpam-6387	220	14	and	and	CCONJ
ejpam-6387	220	15	c	c	NOUN
ejpam-6387	220	16	=	=	SYM
ejpam-6387	220	17	2	2	NUM
ejpam-6387	220	18	on	on	ADP
ejpam-6387	220	19	the	the	DET
ejpam-6387	220	20	error	error	NOUN
ejpam-6387	220	21	term	term	NOUN
ejpam-6387	220	22	of	of	ADP
ejpam-6387	220	23	np(x	np(x	NOUN
ejpam-6387	220	24	)	)	PUNCT
ejpam-6387	220	25	by	by	ADP
ejpam-6387	220	26	the	the	DET
ejpam-6387	220	27	following	following	ADJ
ejpam-6387	220	28	lemmas	lemmas	PROPN
ejpam-6387	220	29	:	:	PUNCT
ejpam-6387	220	30	lemma	lemma	PROPN
ejpam-6387	220	31	2	2	X
ejpam-6387	220	32	.	.	PUNCT
ejpam-6387	220	33	suppose	suppose	VERB
ejpam-6387	220	34	ζp(s	ζp(s	NOUN
ejpam-6387	220	35	)	)	PUNCT
ejpam-6387	220	36	has	have	VERB
ejpam-6387	220	37	an	an	DET
ejpam-6387	220	38	analytic	analytic	ADJ
ejpam-6387	220	39	continuation	continuation	NOUN
ejpam-6387	220	40	to	to	ADP
ejpam-6387	220	41	the	the	DET
ejpam-6387	220	42	half	half	ADJ
ejpam-6387	220	43	plane	plane	NOUN
ejpam-6387	220	44	hα	hα	VERB
ejpam-6387	220	45	except	except	SCONJ
ejpam-6387	220	46	for	for	ADP
ejpam-6387	220	47	a	a	DET
ejpam-6387	220	48	simple	simple	ADJ
ejpam-6387	220	49	pole	pole	NOUN
ejpam-6387	220	50	at	at	ADP
ejpam-6387	220	51	s	s	NOUN
ejpam-6387	220	52	=	=	NOUN
ejpam-6387	220	53	1	1	NUM
ejpam-6387	220	54	with	with	ADP
ejpam-6387	220	55	residue	residue	NOUN
ejpam-6387	220	56	β	β	NOUN
ejpam-6387	220	57	,	,	PUNCT
ejpam-6387	220	58	and	and	CCONJ
ejpam-6387	220	59	ζp(σ+	ζp(σ+	VERB
ejpam-6387	220	60	it	it	PRON
ejpam-6387	220	61	)	)	PUNCT
ejpam-6387	221	1	=	=	PUNCT
ejpam-6387	221	2	o(tc	o(tc	NOUN
ejpam-6387	221	3	)	)	PUNCT
ejpam-6387	221	4	where	where	SCONJ
ejpam-6387	221	5	c	c	NOUN
ejpam-6387	221	6	=	=	SYM
ejpam-6387	221	7	1	1	NUM
ejpam-6387	221	8	and	and	CCONJ
ejpam-6387	221	9	σ	σ	PROPN
ejpam-6387	221	10	≥	≥	PROPN
ejpam-6387	221	11	1−	1−	NUM
ejpam-6387	221	12	1	1	NUM
ejpam-6387	221	13	f(log	f(log	PROPN
ejpam-6387	221	14	t	t	PROPN
ejpam-6387	221	15	)	)	PUNCT
ejpam-6387	221	16	,	,	PUNCT
ejpam-6387	221	17	then	then	ADV
ejpam-6387	221	18	for	for	ADP
ejpam-6387	221	19	γ	γ	X
ejpam-6387	221	20	=	=	SYM
ejpam-6387	221	21	1−	1−	NUM
ejpam-6387	221	22	c	c	NOUN
ejpam-6387	221	23	,	,	PUNCT
ejpam-6387	221	24	np(x	np(x	NUM
ejpam-6387	221	25	)	)	PUNCT
ejpam-6387	221	26	diverges	diverge	NOUN
ejpam-6387	221	27	.	.	PUNCT
ejpam-6387	222	1	proof	proof	NOUN
ejpam-6387	222	2	.	.	PUNCT
ejpam-6387	223	1	since	since	SCONJ
ejpam-6387	223	2	c	c	NOUN
ejpam-6387	223	3	=	=	SYM
ejpam-6387	223	4	1	1	NUM
ejpam-6387	223	5	,	,	PUNCT
ejpam-6387	223	6	then	then	ADV
ejpam-6387	223	7	γ	γ	X
ejpam-6387	223	8	=	=	SYM
ejpam-6387	223	9	0	0	NUM
ejpam-6387	223	10	.	.	PUNCT
ejpam-6387	224	1	after	after	ADP
ejpam-6387	224	2	the	the	DET
ejpam-6387	224	3	same	same	ADJ
ejpam-6387	224	4	calculation	calculation	NOUN
ejpam-6387	224	5	as	as	ADP
ejpam-6387	224	6	c	c	NOUN
ejpam-6387	224	7	=	=	SYM
ejpam-6387	224	8	1/2	1/2	NUM
ejpam-6387	224	9	,	,	PUNCT
ejpam-6387	224	10	we	we	PRON
ejpam-6387	224	11	get	get	VERB
ejpam-6387	224	12	the	the	DET
ejpam-6387	224	13	following	follow	VERB
ejpam-6387	224	14	equation	equation	NOUN
ejpam-6387	224	15	∣∣∣∣zp(x)−	∣∣∣∣zp(x)−	PROPN
ejpam-6387	224	16	β	β	X
ejpam-6387	224	17	2	2	NUM
ejpam-6387	224	18	x2	x2	PROPN
ejpam-6387	224	19	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6387	225	1	=	=	NOUN
ejpam-6387	225	2	o	o	PROPN
ejpam-6387	225	3	(	(	PUNCT
ejpam-6387	225	4	x2	x2	NOUN
ejpam-6387	225	5	∫	∫	PROPN
ejpam-6387	226	1	∞	∞	PROPN
ejpam-6387	226	2	log	log	VERB
ejpam-6387	226	3	a	a	DET
ejpam-6387	226	4	exp(−	exp(−	ADJ
ejpam-6387	226	5	log	log	NOUN
ejpam-6387	226	6	x	x	PUNCT
ejpam-6387	226	7	f(u	f(u	PROPN
ejpam-6387	226	8	)	)	PUNCT
ejpam-6387	226	9	)	)	PUNCT
ejpam-6387	226	10	du	du	PROPN
ejpam-6387	226	11	)	)	PUNCT
ejpam-6387	226	12	as	as	SCONJ
ejpam-6387	226	13	f	f	PROPN
ejpam-6387	226	14	is	be	AUX
ejpam-6387	226	15	increasing	increase	VERB
ejpam-6387	226	16	and	and	CCONJ
ejpam-6387	226	17	goes	go	VERB
ejpam-6387	226	18	to	to	ADP
ejpam-6387	226	19	infinity	infinity	NOUN
ejpam-6387	226	20	,	,	PUNCT
ejpam-6387	226	21	we	we	PRON
ejpam-6387	226	22	get	get	VERB
ejpam-6387	226	23	o	o	NOUN
ejpam-6387	227	1	(	(	PUNCT
ejpam-6387	227	2	x2	x2	NOUN
ejpam-6387	227	3	∫	∫	PROPN
ejpam-6387	227	4	∞	∞	PROPN
ejpam-6387	227	5	log	log	VERB
ejpam-6387	227	6	a	a	DET
ejpam-6387	227	7	1du	1du	NOUN
ejpam-6387	227	8	)	)	PUNCT
ejpam-6387	228	1	−→	−→	NOUN
ejpam-6387	228	2	∞	∞	NUM
ejpam-6387	228	3	hence	hence	ADV
ejpam-6387	228	4	np(x	np(x	NUM
ejpam-6387	228	5	)	)	PUNCT
ejpam-6387	228	6	diverges	diverge	NOUN
ejpam-6387	228	7	.	.	PUNCT
ejpam-6387	229	1	lemma	lemma	PROPN
ejpam-6387	229	2	3	3	X
ejpam-6387	229	3	.	.	PUNCT
ejpam-6387	229	4	suppose	suppose	VERB
ejpam-6387	229	5	ζp(s	ζp(s	NOUN
ejpam-6387	229	6	)	)	PUNCT
ejpam-6387	229	7	has	have	VERB
ejpam-6387	229	8	an	an	DET
ejpam-6387	229	9	analytic	analytic	ADJ
ejpam-6387	229	10	continuation	continuation	NOUN
ejpam-6387	229	11	to	to	ADP
ejpam-6387	229	12	the	the	DET
ejpam-6387	229	13	half	half	ADJ
ejpam-6387	229	14	plane	plane	NOUN
ejpam-6387	229	15	hα	hα	VERB
ejpam-6387	229	16	except	except	SCONJ
ejpam-6387	229	17	for	for	ADP
ejpam-6387	229	18	a	a	DET
ejpam-6387	229	19	simple	simple	ADJ
ejpam-6387	229	20	pole	pole	NOUN
ejpam-6387	229	21	at	at	ADP
ejpam-6387	229	22	s	s	NOUN
ejpam-6387	229	23	=	=	NOUN
ejpam-6387	229	24	1	1	NUM
ejpam-6387	229	25	with	with	ADP
ejpam-6387	229	26	residue	residue	NOUN
ejpam-6387	229	27	β	β	NOUN
ejpam-6387	229	28	,	,	PUNCT
ejpam-6387	229	29	and	and	CCONJ
ejpam-6387	229	30	ζp(σ+	ζp(σ+	VERB
ejpam-6387	229	31	it	it	PRON
ejpam-6387	229	32	)	)	PUNCT
ejpam-6387	230	1	=	=	PUNCT
ejpam-6387	230	2	o(tc	o(tc	NOUN
ejpam-6387	230	3	)	)	PUNCT
ejpam-6387	230	4	where	where	SCONJ
ejpam-6387	230	5	c	c	NOUN
ejpam-6387	230	6	=	=	SYM
ejpam-6387	230	7	2	2	NUM
ejpam-6387	230	8	and	and	CCONJ
ejpam-6387	230	9	σ	σ	PROPN
ejpam-6387	230	10	≥	≥	PROPN
ejpam-6387	230	11	1−	1−	NUM
ejpam-6387	230	12	1	1	NUM
ejpam-6387	230	13	f(log	f(log	PROPN
ejpam-6387	230	14	t	t	PROPN
ejpam-6387	230	15	)	)	PUNCT
ejpam-6387	230	16	,	,	PUNCT
ejpam-6387	230	17	then	then	ADV
ejpam-6387	230	18	np(x	np(x	NUM
ejpam-6387	230	19	)	)	PUNCT
ejpam-6387	230	20	diverges	diverge	NOUN
ejpam-6387	230	21	.	.	PUNCT
ejpam-6387	231	1	z.	z.	PROPN
ejpam-6387	231	2	m.	m.	PROPN
ejpam-6387	231	3	amen	amen	PROPN
ejpam-6387	231	4	,	,	PUNCT
ejpam-6387	231	5	f.	f.	PROPN
ejpam-6387	231	6	a.	a.	PROPN
ejpam-6387	231	7	al	al	PROPN
ejpam-6387	231	8	-	-	PUNCT
ejpam-6387	231	9	maamori	maamori	PROPN
ejpam-6387	231	10	,	,	PUNCT
ejpam-6387	231	11	m.	m.	NOUN
ejpam-6387	231	12	f.	f.	PROPN
ejpam-6387	231	13	hama	hama	PROPN
ejpam-6387	231	14	/	/	SYM
ejpam-6387	231	15	eur	eur	PROPN
ejpam-6387	231	16	.	.	PUNCT
ejpam-6387	232	1	j.	j.	PROPN
ejpam-6387	232	2	pure	pure	PROPN
ejpam-6387	232	3	appl	appl	PROPN
ejpam-6387	232	4	.	.	PROPN
ejpam-6387	232	5	math	math	PROPN
ejpam-6387	232	6	,	,	PUNCT
ejpam-6387	232	7	18	18	NUM
ejpam-6387	232	8	(	(	PUNCT
ejpam-6387	232	9	4	4	NUM
ejpam-6387	232	10	)	)	PUNCT
ejpam-6387	232	11	(	(	PUNCT
ejpam-6387	232	12	2025	2025	NUM
ejpam-6387	232	13	)	)	PUNCT
ejpam-6387	232	14	,	,	PUNCT
ejpam-6387	232	15	6387	6387	NUM
ejpam-6387	232	16	12	12	NUM
ejpam-6387	232	17	of	of	ADP
ejpam-6387	232	18	15	15	NUM
ejpam-6387	232	19	proof	proof	NOUN
ejpam-6387	232	20	.	.	PUNCT
ejpam-6387	233	1	since	since	SCONJ
ejpam-6387	233	2	the	the	DET
ejpam-6387	233	3	third	third	ADJ
ejpam-6387	233	4	term	term	NOUN
ejpam-6387	233	5	of	of	ADP
ejpam-6387	233	6	equation	equation	NOUN
ejpam-6387	233	7	(	(	PUNCT
ejpam-6387	233	8	2	2	X
ejpam-6387	233	9	)	)	PUNCT
ejpam-6387	233	10	is	be	AUX
ejpam-6387	233	11	o	o	NOUN
ejpam-6387	233	12	(	(	PUNCT
ejpam-6387	233	13	xb+1	xb+1	PRON
ejpam-6387	233	14	log	log	VERB
ejpam-6387	233	15	x	x	X
ejpam-6387	233	16	)	)	PUNCT
ejpam-6387	233	17	which	which	PRON
ejpam-6387	233	18	is	be	AUX
ejpam-6387	233	19	constant	constant	ADJ
ejpam-6387	233	20	and∣∣∣∣zp(x)−	and∣∣∣∣zp(x)−	PROPN
ejpam-6387	233	21	β	β	PROPN
ejpam-6387	233	22	2	2	NUM
ejpam-6387	233	23	x2	x2	PROPN
ejpam-6387	233	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6387	233	25	=	=	NOUN
ejpam-6387	233	26	o	o	PROPN
ejpam-6387	233	27	(	(	PUNCT
ejpam-6387	233	28	x2	x2	NOUN
ejpam-6387	233	29	∫	∫	PROPN
ejpam-6387	234	1	∞	∞	PROPN
ejpam-6387	234	2	log	log	VERB
ejpam-6387	234	3	a	a	DET
ejpam-6387	234	4	x	x	SYM
ejpam-6387	234	5	−	−	PROPN
ejpam-6387	234	6	1	1	NUM
ejpam-6387	234	7	f(u	f(u	PROPN
ejpam-6387	234	8	)	)	PUNCT
ejpam-6387	234	9	exp(u)du	exp(u)du	CCONJ
ejpam-6387	234	10	)	)	PUNCT
ejpam-6387	234	11	as	as	SCONJ
ejpam-6387	234	12	f	f	PROPN
ejpam-6387	234	13	is	be	AUX
ejpam-6387	234	14	increasing	increase	VERB
ejpam-6387	234	15	and	and	CCONJ
ejpam-6387	234	16	goes	go	VERB
ejpam-6387	234	17	to	to	ADP
ejpam-6387	234	18	infinity	infinity	NOUN
ejpam-6387	234	19	,	,	PUNCT
ejpam-6387	234	20	we	we	PRON
ejpam-6387	234	21	get	get	VERB
ejpam-6387	234	22	o	o	NOUN
ejpam-6387	234	23	(	(	PUNCT
ejpam-6387	234	24	x2	x2	NOUN
ejpam-6387	234	25	∫	∫	PROPN
ejpam-6387	235	1	∞	∞	PROPN
ejpam-6387	235	2	log	log	VERB
ejpam-6387	235	3	a	a	DET
ejpam-6387	235	4	exp(u)du	exp(u)du	NOUN
ejpam-6387	235	5	)	)	PUNCT
ejpam-6387	235	6	−→	−→	NOUN
ejpam-6387	235	7	∞	∞	NUM
ejpam-6387	235	8	hence	hence	ADV
ejpam-6387	235	9	np(x	np(x	NUM
ejpam-6387	235	10	)	)	PUNCT
ejpam-6387	235	11	diverges	diverge	NOUN
ejpam-6387	235	12	.	.	PUNCT
ejpam-6387	236	1	remark	remark	NOUN
ejpam-6387	236	2	1	1	NUM
ejpam-6387	236	3	.	.	PUNCT
ejpam-6387	237	1	for	for	ADP
ejpam-6387	237	2	c	c	PROPN
ejpam-6387	237	3	>	>	X
ejpam-6387	237	4	2	2	NUM
ejpam-6387	237	5	,	,	PUNCT
ejpam-6387	237	6	np(x	np(x	NUM
ejpam-6387	237	7	)	)	PUNCT
ejpam-6387	237	8	goes	go	VERB
ejpam-6387	237	9	to	to	ADP
ejpam-6387	237	10	∞	∞	PROPN
ejpam-6387	237	11	since	since	SCONJ
ejpam-6387	237	12	the	the	DET
ejpam-6387	237	13	third	third	ADJ
ejpam-6387	237	14	term	term	NOUN
ejpam-6387	237	15	of	of	ADP
ejpam-6387	237	16	equation	equation	NOUN
ejpam-6387	237	17	(	(	PUNCT
ejpam-6387	237	18	2	2	X
ejpam-6387	237	19	)	)	PUNCT
ejpam-6387	237	20	goes	go	VERB
ejpam-6387	237	21	to	to	ADP
ejpam-6387	237	22	∞	∞	NUM
ejpam-6387	237	23	which	which	PRON
ejpam-6387	237	24	leads	lead	VERB
ejpam-6387	237	25	to	to	ADP
ejpam-6387	237	26	np(x	np(x	NUM
ejpam-6387	237	27	)	)	PUNCT
ejpam-6387	237	28	to	to	PART
ejpam-6387	237	29	be	be	AUX
ejpam-6387	237	30	∞.	∞.	PROPN
ejpam-6387	237	31	it	it	PRON
ejpam-6387	237	32	’s	’	VERB
ejpam-6387	237	33	worthwhile	worthwhile	ADJ
ejpam-6387	237	34	to	to	PART
ejpam-6387	237	35	mention	mention	VERB
ejpam-6387	237	36	again	again	ADV
ejpam-6387	237	37	that	that	SCONJ
ejpam-6387	237	38	the	the	DET
ejpam-6387	237	39	effection	effection	NOUN
ejpam-6387	237	40	of	of	ADP
ejpam-6387	237	41	c	c	PROPN
ejpam-6387	237	42	on	on	ADP
ejpam-6387	237	43	the	the	DET
ejpam-6387	237	44	error	error	NOUN
ejpam-6387	237	45	term	term	NOUN
ejpam-6387	237	46	of	of	ADP
ejpam-6387	237	47	np(x	np(x	NOUN
ejpam-6387	237	48	)	)	PUNCT
ejpam-6387	237	49	is	be	AUX
ejpam-6387	237	50	positive	positive	ADJ
ejpam-6387	237	51	and	and	CCONJ
ejpam-6387	237	52	big	big	ADJ
ejpam-6387	237	53	when	when	SCONJ
ejpam-6387	237	54	1	1	NUM
ejpam-6387	237	55	<	<	X
ejpam-6387	237	56	c	c	X
ejpam-6387	237	57	<	<	X
ejpam-6387	237	58	2	2	NUM
ejpam-6387	237	59	,	,	PUNCT
ejpam-6387	237	60	but	but	CCONJ
ejpam-6387	237	61	by	by	ADP
ejpam-6387	237	62	adding	add	VERB
ejpam-6387	237	63	the	the	DET
ejpam-6387	237	64	condition	condition	NOUN
ejpam-6387	237	65	for	for	SCONJ
ejpam-6387	237	66	f	f	PROPN
ejpam-6387	237	67	to	to	PART
ejpam-6387	237	68	be	be	AUX
ejpam-6387	237	69	even	even	ADV
ejpam-6387	237	70	in	in	ADP
ejpam-6387	237	71	theorem	theorem	ADJ
ejpam-6387	237	72	(	(	PUNCT
ejpam-6387	237	73	1	1	NUM
ejpam-6387	237	74	)	)	PUNCT
ejpam-6387	237	75	the	the	DET
ejpam-6387	237	76	error	error	NOUN
ejpam-6387	237	77	term	term	NOUN
ejpam-6387	237	78	will	will	AUX
ejpam-6387	237	79	decrease	decrease	VERB
ejpam-6387	237	80	as	as	SCONJ
ejpam-6387	237	81	shown	show	VERB
ejpam-6387	237	82	in	in	ADP
ejpam-6387	237	83	the	the	DET
ejpam-6387	237	84	following	follow	VERB
ejpam-6387	237	85	lemma	lemma	PROPN
ejpam-6387	237	86	lemma	lemma	PROPN
ejpam-6387	237	87	4	4	X
ejpam-6387	237	88	.	.	PUNCT
ejpam-6387	237	89	suppose	suppose	VERB
ejpam-6387	237	90	for	for	ADP
ejpam-6387	237	91	some	some	DET
ejpam-6387	237	92	α	α	NOUN
ejpam-6387	237	93	∈	∈	PROPN
ejpam-6387	237	94	(	(	PUNCT
ejpam-6387	237	95	0	0	NUM
ejpam-6387	237	96	,	,	PUNCT
ejpam-6387	237	97	1	1	NUM
ejpam-6387	237	98	)	)	PUNCT
ejpam-6387	237	99	,	,	PUNCT
ejpam-6387	237	100	ζp(s	ζp(s	NUM
ejpam-6387	237	101	)	)	PUNCT
ejpam-6387	237	102	has	have	VERB
ejpam-6387	237	103	analytic	analytic	ADJ
ejpam-6387	237	104	continuation	continuation	NOUN
ejpam-6387	237	105	to	to	ADP
ejpam-6387	237	106	the	the	DET
ejpam-6387	237	107	half	half	ADJ
ejpam-6387	237	108	plane	plane	NOUN
ejpam-6387	237	109	hα	hα	VERB
ejpam-6387	237	110	except	except	SCONJ
ejpam-6387	237	111	for	for	ADP
ejpam-6387	237	112	a	a	DET
ejpam-6387	237	113	simple	simple	ADJ
ejpam-6387	237	114	pole	pole	NOUN
ejpam-6387	237	115	at	at	ADP
ejpam-6387	237	116	s	s	NOUN
ejpam-6387	237	117	=	=	NOUN
ejpam-6387	237	118	1	1	NUM
ejpam-6387	237	119	with	with	ADP
ejpam-6387	237	120	residue	residue	NOUN
ejpam-6387	237	121	β	β	NOUN
ejpam-6387	237	122	.	.	PUNCT
ejpam-6387	238	1	furthermore	furthermore	ADV
ejpam-6387	238	2	assume	assume	VERB
ejpam-6387	238	3	that	that	SCONJ
ejpam-6387	238	4	for	for	ADP
ejpam-6387	238	5	1	1	NUM
ejpam-6387	238	6	<	<	X
ejpam-6387	238	7	c	c	X
ejpam-6387	238	8	<	<	X
ejpam-6387	238	9	2	2	NUM
ejpam-6387	238	10	,	,	PUNCT
ejpam-6387	238	11	ζp(s	ζp(s	NUM
ejpam-6387	238	12	)	)	PUNCT
ejpam-6387	238	13	=	=	SYM
ejpam-6387	238	14	o(tc	o(tc	NOUN
ejpam-6387	238	15	)	)	PUNCT
ejpam-6387	238	16	for	for	ADP
ejpam-6387	238	17	σ	σ	PROPN
ejpam-6387	238	18	≥	≥	PROPN
ejpam-6387	238	19	1−	1−	NUM
ejpam-6387	238	20	1	1	NUM
ejpam-6387	238	21	f(log	f(log	PROPN
ejpam-6387	238	22	t	t	PROPN
ejpam-6387	238	23	)	)	PUNCT
ejpam-6387	238	24	,	,	PUNCT
ejpam-6387	238	25	where	where	SCONJ
ejpam-6387	238	26	f	f	PROPN
ejpam-6387	238	27	is	be	AUX
ejpam-6387	238	28	positive	positive	ADJ
ejpam-6387	238	29	,	,	PUNCT
ejpam-6387	238	30	strictly	strictly	ADV
ejpam-6387	238	31	increasing	increase	VERB
ejpam-6387	238	32	continuous	continuous	ADJ
ejpam-6387	238	33	,	,	PUNCT
ejpam-6387	238	34	even	even	ADV
ejpam-6387	238	35	function	function	VERB
ejpam-6387	238	36	and	and	CCONJ
ejpam-6387	238	37	tends	tend	VERB
ejpam-6387	238	38	to	to	PART
ejpam-6387	238	39	infinity	infinity	VERB
ejpam-6387	238	40	then	then	ADV
ejpam-6387	238	41	np(x	np(x	NUM
ejpam-6387	238	42	)	)	PUNCT
ejpam-6387	238	43	=	=	SYM
ejpam-6387	238	44	βx+o	βx+o	PROPN
ejpam-6387	238	45	(	(	PUNCT
ejpam-6387	238	46	x	x	SYM
ejpam-6387	238	47	exp	exp	X
ejpam-6387	238	48	(	(	PUNCT
ejpam-6387	238	49	+	+	CCONJ
ejpam-6387	238	50	γ	γ	X
ejpam-6387	238	51	2	2	NUM
ejpam-6387	238	52	h−1(k	h−1(k	NOUN
ejpam-6387	238	53	log	log	NOUN
ejpam-6387	238	54	x	x	NOUN
ejpam-6387	238	55	)	)	PUNCT
ejpam-6387	238	56	)	)	PUNCT
ejpam-6387	238	57	)	)	PUNCT
ejpam-6387	238	58	,	,	PUNCT
ejpam-6387	238	59	where	where	SCONJ
ejpam-6387	238	60	h(u	h(u	NOUN
ejpam-6387	238	61	)	)	PUNCT
ejpam-6387	238	62	=	=	SYM
ejpam-6387	239	1	uf(u	uf(u	NUM
ejpam-6387	239	2	)	)	PUNCT
ejpam-6387	239	3	,	,	PUNCT
ejpam-6387	239	4	γ	γ	X
ejpam-6387	239	5	=	=	SYM
ejpam-6387	239	6	1−	1−	NUM
ejpam-6387	239	7	c	c	NOUN
ejpam-6387	239	8	<	<	X
ejpam-6387	239	9	0	0	PUNCT
ejpam-6387	239	10	and	and	CCONJ
ejpam-6387	239	11	k	k	NOUN
ejpam-6387	239	12	=	=	PUNCT
ejpam-6387	240	1	−γ−1	−γ−1	X
ejpam-6387	240	2	.	.	PUNCT
ejpam-6387	241	1	proof	proof	NOUN
ejpam-6387	241	2	.	.	PUNCT
ejpam-6387	242	1	by	by	ADP
ejpam-6387	242	2	theorem	theorem	NOUN
ejpam-6387	242	3	(	(	PUNCT
ejpam-6387	242	4	1	1	NUM
ejpam-6387	242	5	)	)	PUNCT
ejpam-6387	242	6	np(x	np(x	NUM
ejpam-6387	242	7	)	)	PUNCT
ejpam-6387	242	8	=	=	SYM
ejpam-6387	242	9	βx+o	βx+o	PROPN
ejpam-6387	242	10	(	(	PUNCT
ejpam-6387	242	11	x	x	SYM
ejpam-6387	242	12	exp	exp	NOUN
ejpam-6387	242	13	(	(	PUNCT
ejpam-6387	242	14	−γ	−γ	ADJ
ejpam-6387	242	15	2h	2h	NUM
ejpam-6387	242	16	−1(γ−1	−1(γ−1	NUM
ejpam-6387	242	17	log	log	NOUN
ejpam-6387	242	18	x	x	NOUN
ejpam-6387	242	19	)	)	PUNCT
ejpam-6387	242	20	)	)	PUNCT
ejpam-6387	242	21	)	)	PUNCT
ejpam-6387	242	22	for	for	ADP
ejpam-6387	242	23	0	0	NUM
ejpam-6387	242	24	<	<	X
ejpam-6387	242	25	c	c	X
ejpam-6387	242	26	<	<	X
ejpam-6387	242	27	1	1	NUM
ejpam-6387	242	28	if	if	SCONJ
ejpam-6387	242	29	1	1	NUM
ejpam-6387	242	30	<	<	X
ejpam-6387	242	31	c	c	X
ejpam-6387	242	32	<	<	X
ejpam-6387	242	33	2	2	NUM
ejpam-6387	242	34	,	,	PUNCT
ejpam-6387	242	35	then	then	ADV
ejpam-6387	242	36	γ	γ	X
ejpam-6387	242	37	=	=	PUNCT
ejpam-6387	242	38	−(1−	−(1−	ADP
ejpam-6387	242	39	c	c	NOUN
ejpam-6387	242	40	)	)	PUNCT
ejpam-6387	242	41	>	>	X
ejpam-6387	242	42	0	0	PUNCT
ejpam-6387	242	43	and	and	CCONJ
ejpam-6387	242	44	γ−1	γ−1	PROPN
ejpam-6387	242	45	=	=	SYM
ejpam-6387	242	46	1	1	NUM
ejpam-6387	242	47	1−c	1−c	NUM
ejpam-6387	242	48	<	<	X
ejpam-6387	242	49	0	0	PUNCT
ejpam-6387	242	50	let	let	VERB
ejpam-6387	242	51	−k	−k	NOUN
ejpam-6387	242	52	=	=	PUNCT
ejpam-6387	242	53	γ−1	γ−1	PROPN
ejpam-6387	242	54	where	where	SCONJ
ejpam-6387	242	55	k	k	PROPN
ejpam-6387	242	56	>	>	X
ejpam-6387	242	57	0	0	PUNCT
ejpam-6387	243	1	and	and	CCONJ
ejpam-6387	243	2	h−1	h−1	PROPN
ejpam-6387	243	3	is	be	AUX
ejpam-6387	243	4	odd	odd	ADJ
ejpam-6387	243	5	(	(	PUNCT
ejpam-6387	243	6	since	since	SCONJ
ejpam-6387	243	7	f	f	PROPN
ejpam-6387	243	8	is	be	AUX
ejpam-6387	243	9	even	even	ADV
ejpam-6387	243	10	)	)	PUNCT
ejpam-6387	243	11	.	.	PUNCT
ejpam-6387	244	1	hence	hence	ADV
ejpam-6387	244	2	np(x	np(x	NUM
ejpam-6387	244	3	)	)	PUNCT
ejpam-6387	244	4	=	=	SYM
ejpam-6387	245	1	βx+o	βx+o	PROPN
ejpam-6387	245	2	(	(	PUNCT
ejpam-6387	245	3	x	x	SYM
ejpam-6387	245	4	exp	exp	NOUN
ejpam-6387	245	5	(	(	PUNCT
ejpam-6387	245	6	−γ	−γ	ADP
ejpam-6387	245	7	2	2	NUM
ejpam-6387	245	8	h−1(−k	h−1(−k	NOUN
ejpam-6387	245	9	log	log	NOUN
ejpam-6387	245	10	x	x	NOUN
ejpam-6387	245	11	)	)	PUNCT
ejpam-6387	245	12	)	)	PUNCT
ejpam-6387	245	13	)	)	PUNCT
ejpam-6387	246	1	=	=	SYM
ejpam-6387	246	2	βx+o	βx+o	PROPN
ejpam-6387	246	3	(	(	PUNCT
ejpam-6387	246	4	x	x	SYM
ejpam-6387	246	5	exp	exp	X
ejpam-6387	246	6	(	(	PUNCT
ejpam-6387	246	7	γ	γ	X
ejpam-6387	246	8	2	2	NUM
ejpam-6387	246	9	h−1(k	h−1(k	NOUN
ejpam-6387	246	10	log	log	NOUN
ejpam-6387	246	11	x	x	NOUN
ejpam-6387	246	12	)	)	PUNCT
ejpam-6387	246	13	)	)	PUNCT
ejpam-6387	246	14	)	)	PUNCT
ejpam-6387	246	15	where	where	SCONJ
ejpam-6387	246	16	γ	γ	X
ejpam-6387	246	17	=	=	SYM
ejpam-6387	246	18	1−	1−	NUM
ejpam-6387	246	19	c	c	NOUN
ejpam-6387	246	20	<	<	X
ejpam-6387	246	21	0	0	NUM
ejpam-6387	246	22	for	for	ADP
ejpam-6387	246	23	1	1	NUM
ejpam-6387	246	24	<	<	X
ejpam-6387	246	25	c	c	X
ejpam-6387	246	26	<	<	X
ejpam-6387	246	27	2	2	NUM
ejpam-6387	246	28	the	the	DET
ejpam-6387	246	29	following	follow	VERB
ejpam-6387	246	30	is	be	AUX
ejpam-6387	246	31	the	the	DET
ejpam-6387	246	32	counter	counter	ADJ
ejpam-6387	246	33	example	example	NOUN
ejpam-6387	246	34	to	to	PART
ejpam-6387	246	35	apply	apply	VERB
ejpam-6387	246	36	theorem(2	theorem(2	NUM
ejpam-6387	246	37	)	)	PUNCT
ejpam-6387	246	38	.	.	PUNCT
ejpam-6387	247	1	example	example	NOUN
ejpam-6387	248	1	1	1	X
ejpam-6387	248	2	.	.	PUNCT
ejpam-6387	248	3	let	let	VERB
ejpam-6387	248	4	f(x	f(x	PROPN
ejpam-6387	248	5	)	)	PUNCT
ejpam-6387	249	1	=	=	SYM
ejpam-6387	250	1	xn	xn	NUM
ejpam-6387	251	1	log	log	NOUN
ejpam-6387	252	1	x	x	INTJ
ejpam-6387	252	2	.	.	PUNCT
ejpam-6387	253	1	then	then	ADV
ejpam-6387	253	2	h(x	h(x	PROPN
ejpam-6387	253	3	)	)	PUNCT
ejpam-6387	253	4	=	=	PUNCT
ejpam-6387	254	1	xn+1	xn+1	NUM
ejpam-6387	254	2	log	log	NOUN
ejpam-6387	254	3	x	x	SYM
ejpam-6387	254	4	,	,	PUNCT
ejpam-6387	254	5	h−1(x	h−1(x	NOUN
ejpam-6387	254	6	)	)	PUNCT
ejpam-6387	254	7	∼	∼	NOUN
ejpam-6387	254	8	n+1	n+1	ADV
ejpam-6387	254	9	√	√	PUNCT
ejpam-6387	254	10	xn	xn	PUNCT
ejpam-6387	255	1	log	log	PROPN
ejpam-6387	255	2	x	x	NOUN
ejpam-6387	255	3	n+1	n+1	PROPN
ejpam-6387	255	4	,	,	PUNCT
ejpam-6387	255	5	and	and	CCONJ
ejpam-6387	255	6	h−1(log	h−1(log	NOUN
ejpam-6387	255	7	x	x	X
ejpam-6387	255	8	)	)	PUNCT
ejpam-6387	255	9	∼	∼	NOUN
ejpam-6387	255	10	n+1	n+1	PUNCT
ejpam-6387	255	11	√	√	NUM
ejpam-6387	255	12	(	(	PUNCT
ejpam-6387	255	13	log	log	PROPN
ejpam-6387	255	14	x)n	x)n	PUNCT
ejpam-6387	255	15	log	log	VERB
ejpam-6387	255	16	log	log	NOUN
ejpam-6387	255	17	x	x	PUNCT
ejpam-6387	255	18	n+1	n+1	ADV
ejpam-6387	255	19	now	now	ADV
ejpam-6387	255	20	if	if	SCONJ
ejpam-6387	255	21	c	c	NOUN
ejpam-6387	255	22	=	=	SYM
ejpam-6387	255	23	1/2	1/2	NUM
ejpam-6387	255	24	,	,	PUNCT
ejpam-6387	255	25	we	we	PRON
ejpam-6387	255	26	have	have	VERB
ejpam-6387	255	27	ζp(σ	ζp(σ	X
ejpam-6387	255	28	+	+	CCONJ
ejpam-6387	255	29	it	it	PRON
ejpam-6387	255	30	)	)	PUNCT
ejpam-6387	256	1	=	=	PUNCT
ejpam-6387	256	2	o(t1/2	o(t1/2	NUM
ejpam-6387	256	3	)	)	PUNCT
ejpam-6387	256	4	for	for	ADP
ejpam-6387	256	5	σ	σ	PROPN
ejpam-6387	256	6	≥	≥	PROPN
ejpam-6387	256	7	1−	1−	NUM
ejpam-6387	256	8	log	log	NOUN
ejpam-6387	256	9	log	log	NOUN
ejpam-6387	256	10	t	t	PROPN
ejpam-6387	256	11	n	n	PRON
ejpam-6387	256	12	log	log	VERB
ejpam-6387	256	13	t	t	PROPN
ejpam-6387	256	14	and	and	CCONJ
ejpam-6387	256	15	np(x	np(x	NUM
ejpam-6387	256	16	)	)	PUNCT
ejpam-6387	256	17	=	=	SYM
ejpam-6387	257	1	ρx+o	ρx+o	NOUN
ejpam-6387	257	2	(	(	PUNCT
ejpam-6387	257	3	x	x	SYM
ejpam-6387	257	4	exp	exp	X
ejpam-6387	257	5	(	(	PUNCT
ejpam-6387	257	6	−1	−1	NOUN
ejpam-6387	257	7	4	4	NUM
ejpam-6387	257	8	n+1	n+1	NUM
ejpam-6387	257	9	√	√	NUM
ejpam-6387	257	10	(	(	PUNCT
ejpam-6387	257	11	2	2	NUM
ejpam-6387	257	12	log	log	NOUN
ejpam-6387	257	13	x)n	x)n	PUNCT
ejpam-6387	257	14	2	2	NUM
ejpam-6387	257	15	log	log	NOUN
ejpam-6387	257	16	log	log	NOUN
ejpam-6387	257	17	x	x	PUNCT
ejpam-6387	257	18	n+	n+	ADP
ejpam-6387	257	19	1	1	NUM
ejpam-6387	257	20	)	)	PUNCT
ejpam-6387	257	21	)	)	PUNCT
ejpam-6387	257	22	.	.	PUNCT
ejpam-6387	258	1	z.	z.	PROPN
ejpam-6387	258	2	m.	m.	PROPN
ejpam-6387	258	3	amen	amen	INTJ
ejpam-6387	258	4	,	,	PUNCT
ejpam-6387	258	5	f.	f.	PROPN
ejpam-6387	258	6	a.	a.	PROPN
ejpam-6387	258	7	al	al	PROPN
ejpam-6387	258	8	-	-	PUNCT
ejpam-6387	258	9	maamori	maamori	PROPN
ejpam-6387	258	10	,	,	PUNCT
ejpam-6387	258	11	m.	m.	NOUN
ejpam-6387	258	12	f.	f.	PROPN
ejpam-6387	258	13	hama	hama	PROPN
ejpam-6387	258	14	/	/	SYM
ejpam-6387	258	15	eur	eur	PROPN
ejpam-6387	258	16	.	.	PUNCT
ejpam-6387	259	1	j.	j.	PROPN
ejpam-6387	259	2	pure	pure	PROPN
ejpam-6387	259	3	appl	appl	PROPN
ejpam-6387	259	4	.	.	PROPN
ejpam-6387	259	5	math	math	PROPN
ejpam-6387	259	6	,	,	PUNCT
ejpam-6387	259	7	18	18	NUM
ejpam-6387	259	8	(	(	PUNCT
ejpam-6387	259	9	4	4	NUM
ejpam-6387	259	10	)	)	PUNCT
ejpam-6387	259	11	(	(	PUNCT
ejpam-6387	259	12	2025	2025	NUM
ejpam-6387	259	13	)	)	PUNCT
ejpam-6387	259	14	,	,	PUNCT
ejpam-6387	259	15	6387	6387	NUM
ejpam-6387	259	16	13	13	NUM
ejpam-6387	259	17	of	of	ADP
ejpam-6387	259	18	15	15	NUM
ejpam-6387	259	19	5	5	NUM
ejpam-6387	259	20	.	.	PUNCT
ejpam-6387	260	1	the	the	DET
ejpam-6387	260	2	connection	connection	NOUN
ejpam-6387	260	3	between	between	ADP
ejpam-6387	260	4	the	the	DET
ejpam-6387	260	5	constant	constant	ADJ
ejpam-6387	260	6	c	c	NOUN
ejpam-6387	260	7	and	and	CCONJ
ejpam-6387	260	8	the	the	DET
ejpam-6387	260	9	real	real	ADJ
ejpam-6387	260	10	part	part	NOUN
ejpam-6387	260	11	σ	σ	NOUN
ejpam-6387	260	12	of	of	ADP
ejpam-6387	260	13	beurling	beurle	VERB
ejpam-6387	260	14	zeta	zeta	PROPN
ejpam-6387	260	15	function	function	NOUN
ejpam-6387	260	16	ζp(s	ζp(s	NOUN
ejpam-6387	260	17	)	)	PUNCT
ejpam-6387	260	18	this	this	DET
ejpam-6387	260	19	part	part	NOUN
ejpam-6387	260	20	concentrated	concentrate	VERB
ejpam-6387	260	21	on	on	ADP
ejpam-6387	260	22	figuring	figure	VERB
ejpam-6387	260	23	out	out	ADP
ejpam-6387	260	24	the	the	DET
ejpam-6387	260	25	connection	connection	NOUN
ejpam-6387	260	26	between	between	ADP
ejpam-6387	260	27	constant	constant	ADJ
ejpam-6387	260	28	c	c	NOUN
ejpam-6387	260	29	in	in	ADP
ejpam-6387	260	30	the	the	DET
ejpam-6387	260	31	order	order	NOUN
ejpam-6387	260	32	of	of	ADP
ejpam-6387	260	33	beurling	beurle	VERB
ejpam-6387	260	34	zeta	zeta	PROPN
ejpam-6387	260	35	function	function	NOUN
ejpam-6387	260	36	ζp(s	ζp(s	NUM
ejpam-6387	260	37	)	)	PUNCT
ejpam-6387	260	38	and	and	CCONJ
ejpam-6387	260	39	σ(the	σ(the	DET
ejpam-6387	260	40	real	real	ADJ
ejpam-6387	260	41	part	part	NOUN
ejpam-6387	260	42	of	of	ADP
ejpam-6387	260	43	beurling	beurle	VERB
ejpam-6387	260	44	zeta	zeta	PROPN
ejpam-6387	260	45	function	function	NOUN
ejpam-6387	260	46	ζp(s	ζp(s	NUM
ejpam-6387	260	47	)	)	PUNCT
ejpam-6387	260	48	)	)	PUNCT
ejpam-6387	260	49	.	.	PUNCT
ejpam-6387	261	1	in	in	ADP
ejpam-6387	261	2	other	other	ADJ
ejpam-6387	261	3	meaning	meaning	NOUN
ejpam-6387	261	4	the	the	DET
ejpam-6387	261	5	reader	reader	NOUN
ejpam-6387	261	6	can	can	AUX
ejpam-6387	261	7	see	see	VERB
ejpam-6387	261	8	earlier	early	ADV
ejpam-6387	261	9	thatt	thatt	VERB
ejpam-6387	261	10	there	there	PRON
ejpam-6387	261	11	is	be	VERB
ejpam-6387	261	12	a	a	DET
ejpam-6387	261	13	connection	connection	NOUN
ejpam-6387	261	14	between	between	ADP
ejpam-6387	261	15	zeta	zeta	NOUN
ejpam-6387	261	16	function	function	NOUN
ejpam-6387	261	17	and	and	CCONJ
ejpam-6387	261	18	beurling	beurle	VERB
ejpam-6387	261	19	integer	integer	NOUN
ejpam-6387	261	20	counting	counting	NOUN
ejpam-6387	261	21	function	function	NOUN
ejpam-6387	261	22	,	,	PUNCT
ejpam-6387	261	23	so	so	ADV
ejpam-6387	261	24	we	we	PRON
ejpam-6387	261	25	are	be	AUX
ejpam-6387	261	26	interested	interested	ADJ
ejpam-6387	261	27	to	to	PART
ejpam-6387	261	28	figure	figure	VERB
ejpam-6387	261	29	out	out	ADP
ejpam-6387	261	30	this	this	DET
ejpam-6387	261	31	type	type	NOUN
ejpam-6387	261	32	of	of	ADP
ejpam-6387	261	33	connection	connection	NOUN
ejpam-6387	261	34	.	.	PUNCT
ejpam-6387	262	1	fore	fore	NOUN
ejpam-6387	262	2	more	more	ADJ
ejpam-6387	262	3	details	detail	NOUN
ejpam-6387	262	4	the	the	DET
ejpam-6387	262	5	reader	reader	NOUN
ejpam-6387	262	6	could	could	AUX
ejpam-6387	262	7	see	see	VERB
ejpam-6387	262	8	(	(	PUNCT
ejpam-6387	262	9	[	[	X
ejpam-6387	262	10	20	20	NUM
ejpam-6387	262	11	]	]	PUNCT
ejpam-6387	262	12	,	,	PUNCT
ejpam-6387	262	13	pp.392	pp.392	PROPN
ejpam-6387	262	14	)	)	PUNCT
ejpam-6387	262	15	.	.	PUNCT
ejpam-6387	263	1	our	our	PRON
ejpam-6387	263	2	aim	aim	NOUN
ejpam-6387	263	3	is	be	AUX
ejpam-6387	263	4	to	to	PART
ejpam-6387	263	5	apply	apply	VERB
ejpam-6387	263	6	theorem	theorem	NOUN
ejpam-6387	263	7	(	(	PUNCT
ejpam-6387	263	8	2	2	NUM
ejpam-6387	263	9	)	)	PUNCT
ejpam-6387	263	10	and	and	CCONJ
ejpam-6387	263	11	have	have	VERB
ejpam-6387	263	12	to	to	PART
ejpam-6387	263	13	show	show	VERB
ejpam-6387	263	14	for	for	ADP
ejpam-6387	263	15	which	which	DET
ejpam-6387	263	16	region	region	NOUN
ejpam-6387	263	17	of	of	ADP
ejpam-6387	263	18	σ	σ	PROPN
ejpam-6387	263	19	,	,	PUNCT
ejpam-6387	263	20	ζ0(σ	ζ0(σ	PROPN
ejpam-6387	263	21	+	+	CCONJ
ejpam-6387	263	22	it	it	PRON
ejpam-6387	263	23	)	)	PUNCT
ejpam-6387	264	1	=	=	PUNCT
ejpam-6387	264	2	o(t1/2	o(t1/2	ADJ
ejpam-6387	264	3	)	)	PUNCT
ejpam-6387	264	4	.	.	PUNCT
ejpam-6387	265	1	so	so	ADV
ejpam-6387	265	2	in	in	ADP
ejpam-6387	265	3	order	order	NOUN
ejpam-6387	265	4	for	for	ADP
ejpam-6387	265	5	|ζ0(σ	|ζ0(σ	PRON
ejpam-6387	265	6	+	+	CCONJ
ejpam-6387	265	7	it)|	it)|	PROPN
ejpam-6387	265	8	�	�	PROPN
ejpam-6387	265	9	tc	tc	NOUN
ejpam-6387	265	10	to	to	PART
ejpam-6387	265	11	hold	hold	VERB
ejpam-6387	265	12	for	for	ADP
ejpam-6387	265	13	c	c	NOUN
ejpam-6387	265	14	=	=	SYM
ejpam-6387	265	15	1	1	NUM
ejpam-6387	265	16	2	2	NUM
ejpam-6387	265	17	,	,	PUNCT
ejpam-6387	265	18	we	we	PRON
ejpam-6387	265	19	have	have	VERB
ejpam-6387	265	20	the	the	DET
ejpam-6387	265	21	following	following	NOUN
ejpam-6387	265	22	:	:	PUNCT
ejpam-6387	265	23	|ζ0(σ	|ζ0(σ	PROPN
ejpam-6387	265	24	+	+	CCONJ
ejpam-6387	265	25	it)|	it)|	PROPN
ejpam-6387	265	26	�	�	PROPN
ejpam-6387	265	27	exp	exp	NOUN
ejpam-6387	265	28	(	(	PUNCT
ejpam-6387	265	29	1	1	NUM
ejpam-6387	265	30	+	+	CCONJ
ejpam-6387	265	31	t100(1−σ	t100(1−σ	X
ejpam-6387	265	32	)	)	PUNCT
ejpam-6387	265	33	3	3	NUM
ejpam-6387	265	34	2	2	NUM
ejpam-6387	265	35	(	(	PUNCT
ejpam-6387	265	36	log	log	NOUN
ejpam-6387	265	37	t	t	PROPN
ejpam-6387	265	38	)	)	PUNCT
ejpam-6387	265	39	2	2	NUM
ejpam-6387	265	40	3	3	NUM
ejpam-6387	265	41	)	)	PUNCT
ejpam-6387	265	42	so	so	ADV
ejpam-6387	265	43	,	,	PUNCT
ejpam-6387	265	44	we	we	PRON
ejpam-6387	265	45	get	get	VERB
ejpam-6387	265	46	exp	exp	NOUN
ejpam-6387	265	47	[	[	X
ejpam-6387	265	48	(	(	PUNCT
ejpam-6387	265	49	1	1	NUM
ejpam-6387	265	50	+	+	CCONJ
ejpam-6387	265	51	t100(1−σ	t100(1−σ	X
ejpam-6387	265	52	)	)	PUNCT
ejpam-6387	265	53	3	3	NUM
ejpam-6387	265	54	2	2	NUM
ejpam-6387	265	55	)	)	PUNCT
ejpam-6387	265	56	(	(	PUNCT
ejpam-6387	265	57	log	log	PROPN
ejpam-6387	265	58	t	t	PROPN
ejpam-6387	265	59	)	)	PUNCT
ejpam-6387	265	60	2	2	NUM
ejpam-6387	265	61	3	3	NUM
ejpam-6387	265	62	]	]	PUNCT
ejpam-6387	265	63	≤	≤	NUM
ejpam-6387	265	64	t	t	NOUN
ejpam-6387	265	65	1	1	NUM
ejpam-6387	265	66	2	2	NUM
ejpam-6387	265	67	(	(	PUNCT
ejpam-6387	265	68	1	1	NUM
ejpam-6387	265	69	+	+	CCONJ
ejpam-6387	265	70	t100(1−σ	t100(1−σ	X
ejpam-6387	265	71	)	)	PUNCT
ejpam-6387	265	72	3	3	NUM
ejpam-6387	265	73	2	2	NUM
ejpam-6387	265	74	)	)	PUNCT
ejpam-6387	265	75	(	(	PUNCT
ejpam-6387	265	76	log	log	PROPN
ejpam-6387	265	77	t	t	PROPN
ejpam-6387	265	78	)	)	PUNCT
ejpam-6387	265	79	2	2	NUM
ejpam-6387	265	80	3	3	NUM
ejpam-6387	265	81	≤	≤	NOUN
ejpam-6387	265	82	log	log	NOUN
ejpam-6387	265	83	t	t	PROPN
ejpam-6387	265	84	1	1	NUM
ejpam-6387	265	85	2	2	NUM
ejpam-6387	265	86	(	(	PUNCT
ejpam-6387	265	87	1	1	NUM
ejpam-6387	265	88	+	+	NUM
ejpam-6387	265	89	e100(1−σ	e100(1−σ	X
ejpam-6387	265	90	)	)	PUNCT
ejpam-6387	265	91	3	3	NUM
ejpam-6387	265	92	2	2	NUM
ejpam-6387	265	93	log	log	NOUN
ejpam-6387	265	94	t	t	NOUN
ejpam-6387	265	95	)	)	PUNCT
ejpam-6387	265	96	≤	≤	NOUN
ejpam-6387	265	97	1	1	NUM
ejpam-6387	265	98	2	2	NUM
ejpam-6387	265	99	(	(	PUNCT
ejpam-6387	265	100	log	log	NOUN
ejpam-6387	265	101	t	t	PROPN
ejpam-6387	265	102	)	)	PUNCT
ejpam-6387	265	103	1	1	NUM
ejpam-6387	265	104	3	3	NUM
ejpam-6387	265	105	e100(1−σ	e100(1−σ	NOUN
ejpam-6387	265	106	)	)	PUNCT
ejpam-6387	265	107	3	3	NUM
ejpam-6387	265	108	2	2	NUM
ejpam-6387	265	109	log	log	NOUN
ejpam-6387	265	110	t	t	NOUN
ejpam-6387	265	111	≤	≤	NUM
ejpam-6387	265	112	1	1	NUM
ejpam-6387	265	113	+	+	NUM
ejpam-6387	265	114	e100(1−σ	e100(1−σ	X
ejpam-6387	265	115	)	)	PUNCT
ejpam-6387	265	116	3	3	NUM
ejpam-6387	265	117	2	2	NUM
ejpam-6387	265	118	log	log	NOUN
ejpam-6387	265	119	t	t	NOUN
ejpam-6387	265	120	≤	≤	NUM
ejpam-6387	265	121	1	1	NUM
ejpam-6387	265	122	2	2	NUM
ejpam-6387	265	123	(	(	PUNCT
ejpam-6387	265	124	log	log	NOUN
ejpam-6387	265	125	t	t	PROPN
ejpam-6387	265	126	)	)	PUNCT
ejpam-6387	265	127	1	1	NUM
ejpam-6387	265	128	3	3	NUM
ejpam-6387	265	129	so	so	ADV
ejpam-6387	265	130	e100(1−σ	e100(1−σ	NOUN
ejpam-6387	265	131	)	)	PUNCT
ejpam-6387	265	132	3	3	NUM
ejpam-6387	265	133	2	2	NUM
ejpam-6387	265	134	log	log	NOUN
ejpam-6387	265	135	t	t	NOUN
ejpam-6387	265	136	≤	≤	NUM
ejpam-6387	265	137	1	1	NUM
ejpam-6387	265	138	2	2	NUM
ejpam-6387	265	139	(	(	PUNCT
ejpam-6387	265	140	log	log	NOUN
ejpam-6387	265	141	t	t	PROPN
ejpam-6387	265	142	)	)	PUNCT
ejpam-6387	265	143	1	1	NUM
ejpam-6387	265	144	3	3	NUM
ejpam-6387	265	145	log	log	NOUN
ejpam-6387	265	146	(	(	PUNCT
ejpam-6387	265	147	e100(1−σ	e100(1−σ	X
ejpam-6387	265	148	)	)	PUNCT
ejpam-6387	265	149	3	3	NUM
ejpam-6387	265	150	2	2	NUM
ejpam-6387	265	151	log	log	NOUN
ejpam-6387	265	152	t	t	PROPN
ejpam-6387	265	153	)	)	PUNCT
ejpam-6387	265	154	≤	≤	NOUN
ejpam-6387	266	1	log	log	NOUN
ejpam-6387	266	2	(	(	PUNCT
ejpam-6387	266	3	1	1	NUM
ejpam-6387	266	4	2	2	NUM
ejpam-6387	266	5	(	(	PUNCT
ejpam-6387	266	6	log	log	NOUN
ejpam-6387	266	7	t	t	PROPN
ejpam-6387	266	8	)	)	PUNCT
ejpam-6387	266	9	1	1	NUM
ejpam-6387	266	10	3	3	NUM
ejpam-6387	266	11	)	)	PUNCT
ejpam-6387	266	12	100(1−	100(1−	NUM
ejpam-6387	266	13	σ	σ	NOUN
ejpam-6387	266	14	)	)	PUNCT
ejpam-6387	266	15	3	3	NUM
ejpam-6387	266	16	2	2	NUM
ejpam-6387	266	17	log	log	NOUN
ejpam-6387	266	18	t	t	PROPN
ejpam-6387	266	19	≤	≤	NUM
ejpam-6387	266	20	log	log	NOUN
ejpam-6387	266	21	(	(	PUNCT
ejpam-6387	266	22	1	1	NUM
ejpam-6387	266	23	2	2	NUM
ejpam-6387	266	24	)	)	PUNCT
ejpam-6387	266	25	+	+	CCONJ
ejpam-6387	266	26	log	log	NOUN
ejpam-6387	266	27	(	(	PUNCT
ejpam-6387	266	28	(	(	PUNCT
ejpam-6387	266	29	log	log	PROPN
ejpam-6387	266	30	t	t	PROPN
ejpam-6387	266	31	)	)	PUNCT
ejpam-6387	266	32	1	1	NUM
ejpam-6387	266	33	3	3	NUM
ejpam-6387	266	34	)	)	PUNCT
ejpam-6387	266	35	(	(	PUNCT
ejpam-6387	266	36	1−	1−	NUM
ejpam-6387	266	37	σ	σ	NOUN
ejpam-6387	266	38	)	)	PUNCT
ejpam-6387	266	39	3	3	NUM
ejpam-6387	266	40	2	2	NUM
ejpam-6387	266	41	≤	≤	NOUN
ejpam-6387	266	42	log	log	VERB
ejpam-6387	266	43	1	1	NUM
ejpam-6387	266	44	2	2	NUM
ejpam-6387	266	45	+	+	CCONJ
ejpam-6387	266	46	1	1	NUM
ejpam-6387	266	47	3	3	NUM
ejpam-6387	266	48	log	log	NOUN
ejpam-6387	266	49	log	log	NOUN
ejpam-6387	266	50	t	t	PROPN
ejpam-6387	266	51	100	100	NUM
ejpam-6387	266	52	log	log	NOUN
ejpam-6387	266	53	t	t	PROPN
ejpam-6387	266	54	log	log	NOUN
ejpam-6387	266	55	(	(	PUNCT
ejpam-6387	266	56	e100(1−σ	e100(1−σ	X
ejpam-6387	266	57	)	)	PUNCT
ejpam-6387	266	58	3	3	NUM
ejpam-6387	266	59	2	2	NUM
ejpam-6387	266	60	log	log	NOUN
ejpam-6387	266	61	t	t	PROPN
ejpam-6387	266	62	)	)	PUNCT
ejpam-6387	266	63	≤	≤	NOUN
ejpam-6387	267	1	log	log	NOUN
ejpam-6387	267	2	(	(	PUNCT
ejpam-6387	267	3	1	1	NUM
ejpam-6387	267	4	2	2	NUM
ejpam-6387	267	5	(	(	PUNCT
ejpam-6387	267	6	log	log	NOUN
ejpam-6387	267	7	t	t	PROPN
ejpam-6387	267	8	)	)	PUNCT
ejpam-6387	267	9	1	1	NUM
ejpam-6387	267	10	3	3	NUM
ejpam-6387	267	11	)	)	PUNCT
ejpam-6387	267	12	100(1−	100(1−	NUM
ejpam-6387	267	13	σ	σ	NOUN
ejpam-6387	267	14	)	)	PUNCT
ejpam-6387	267	15	3	3	NUM
ejpam-6387	267	16	2	2	NUM
ejpam-6387	267	17	log	log	NOUN
ejpam-6387	267	18	t	t	PROPN
ejpam-6387	267	19	≤	≤	NUM
ejpam-6387	267	20	log	log	NOUN
ejpam-6387	267	21	(	(	PUNCT
ejpam-6387	267	22	1	1	NUM
ejpam-6387	267	23	2	2	NUM
ejpam-6387	267	24	)	)	PUNCT
ejpam-6387	267	25	+	+	CCONJ
ejpam-6387	267	26	log	log	NOUN
ejpam-6387	267	27	(	(	PUNCT
ejpam-6387	267	28	(	(	PUNCT
ejpam-6387	267	29	log	log	PROPN
ejpam-6387	267	30	t	t	PROPN
ejpam-6387	267	31	)	)	PUNCT
ejpam-6387	267	32	1	1	NUM
ejpam-6387	267	33	3	3	NUM
ejpam-6387	267	34	)	)	PUNCT
ejpam-6387	267	35	(	(	PUNCT
ejpam-6387	267	36	1−	1−	NUM
ejpam-6387	267	37	σ	σ	NOUN
ejpam-6387	267	38	)	)	PUNCT
ejpam-6387	267	39	3	3	NUM
ejpam-6387	267	40	2	2	NUM
ejpam-6387	267	41	≤	≤	NOUN
ejpam-6387	267	42	log	log	VERB
ejpam-6387	267	43	1	1	NUM
ejpam-6387	267	44	2	2	NUM
ejpam-6387	267	45	+	+	CCONJ
ejpam-6387	267	46	1	1	NUM
ejpam-6387	267	47	3	3	NUM
ejpam-6387	267	48	log	log	NOUN
ejpam-6387	267	49	log	log	NOUN
ejpam-6387	267	50	t	t	PROPN
ejpam-6387	267	51	100	100	NUM
ejpam-6387	267	52	log	log	NOUN
ejpam-6387	267	53	t	t	PROPN
ejpam-6387	267	54	z.	z.	PROPN
ejpam-6387	267	55	m.	m.	PROPN
ejpam-6387	267	56	amen	amen	PROPN
ejpam-6387	267	57	,	,	PUNCT
ejpam-6387	267	58	f.	f.	PROPN
ejpam-6387	267	59	a.	a.	PROPN
ejpam-6387	267	60	al	al	PROPN
ejpam-6387	267	61	-	-	PUNCT
ejpam-6387	267	62	maamori	maamori	PROPN
ejpam-6387	267	63	,	,	PUNCT
ejpam-6387	267	64	m.	m.	NOUN
ejpam-6387	267	65	f.	f.	PROPN
ejpam-6387	267	66	hama	hama	PROPN
ejpam-6387	267	67	/	/	SYM
ejpam-6387	267	68	eur	eur	PROPN
ejpam-6387	267	69	.	.	PUNCT
ejpam-6387	268	1	j.	j.	PROPN
ejpam-6387	268	2	pure	pure	PROPN
ejpam-6387	268	3	appl	appl	PROPN
ejpam-6387	268	4	.	.	PROPN
ejpam-6387	268	5	math	math	PROPN
ejpam-6387	268	6	,	,	PUNCT
ejpam-6387	268	7	18	18	NUM
ejpam-6387	268	8	(	(	PUNCT
ejpam-6387	268	9	4	4	NUM
ejpam-6387	268	10	)	)	PUNCT
ejpam-6387	268	11	(	(	PUNCT
ejpam-6387	268	12	2025	2025	NUM
ejpam-6387	268	13	)	)	PUNCT
ejpam-6387	268	14	,	,	PUNCT
ejpam-6387	268	15	6387	6387	NUM
ejpam-6387	268	16	14	14	NUM
ejpam-6387	268	17	of	of	ADP
ejpam-6387	268	18	15	15	NUM
ejpam-6387	268	19	(	(	PUNCT
ejpam-6387	268	20	1−	1−	NUM
ejpam-6387	268	21	σ	σ	PROPN
ejpam-6387	268	22	)	)	PUNCT
ejpam-6387	268	23	≤	≤	NOUN
ejpam-6387	268	24	(	(	PUNCT
ejpam-6387	268	25	log	log	VERB
ejpam-6387	268	26	1	1	NUM
ejpam-6387	268	27	2	2	NUM
ejpam-6387	268	28	+	+	CCONJ
ejpam-6387	268	29	1	1	NUM
ejpam-6387	268	30	3	3	NUM
ejpam-6387	268	31	log	log	NOUN
ejpam-6387	268	32	log	log	NOUN
ejpam-6387	268	33	t	t	PROPN
ejpam-6387	268	34	100	100	NUM
ejpam-6387	268	35	log	log	NOUN
ejpam-6387	268	36	t	t	PROPN
ejpam-6387	268	37	)	)	PUNCT
ejpam-6387	268	38	2	2	NUM
ejpam-6387	268	39	3	3	NUM
ejpam-6387	268	40	−σ	−σ	NOUN
ejpam-6387	268	41	≤	≤	NUM
ejpam-6387	268	42	−1	−1	NOUN
ejpam-6387	269	1	+	+	CCONJ
ejpam-6387	269	2	(	(	PUNCT
ejpam-6387	269	3	log	log	VERB
ejpam-6387	269	4	1	1	NUM
ejpam-6387	269	5	2	2	NUM
ejpam-6387	269	6	+	+	CCONJ
ejpam-6387	269	7	1	1	NUM
ejpam-6387	269	8	3	3	NUM
ejpam-6387	269	9	log	log	NOUN
ejpam-6387	269	10	log	log	NOUN
ejpam-6387	269	11	t	t	PROPN
ejpam-6387	269	12	100	100	NUM
ejpam-6387	269	13	log	log	NOUN
ejpam-6387	269	14	t	t	PROPN
ejpam-6387	269	15	)	)	PUNCT
ejpam-6387	269	16	2	2	NUM
ejpam-6387	269	17	3	3	NUM
ejpam-6387	269	18	σ	σ	NUM
ejpam-6387	269	19	≥	≥	NOUN
ejpam-6387	269	20	1−	1−	NUM
ejpam-6387	269	21	(	(	PUNCT
ejpam-6387	269	22	log	log	VERB
ejpam-6387	269	23	1	1	NUM
ejpam-6387	269	24	2	2	NUM
ejpam-6387	269	25	+	+	CCONJ
ejpam-6387	269	26	1	1	NUM
ejpam-6387	269	27	3	3	NUM
ejpam-6387	269	28	log	log	NOUN
ejpam-6387	269	29	log	log	NOUN
ejpam-6387	269	30	t	t	PROPN
ejpam-6387	269	31	100	100	NUM
ejpam-6387	269	32	log	log	NOUN
ejpam-6387	269	33	t	t	PROPN
ejpam-6387	269	34	)	)	PUNCT
ejpam-6387	269	35	2	2	NUM
ejpam-6387	269	36	3	3	NUM
ejpam-6387	269	37	hence	hence	ADV
ejpam-6387	269	38	for	for	ADP
ejpam-6387	269	39	the	the	DET
ejpam-6387	269	40	above	above	PROPN
ejpam-6387	269	41	σ	σ	PROPN
ejpam-6387	269	42	,	,	PUNCT
ejpam-6387	269	43	we	we	PRON
ejpam-6387	269	44	have	have	VERB
ejpam-6387	269	45	ζ0(σ	ζ0(σ	X
ejpam-6387	270	1	+	+	CCONJ
ejpam-6387	270	2	it	it	PRON
ejpam-6387	270	3	)	)	PUNCT
ejpam-6387	271	1	=	=	PUNCT
ejpam-6387	272	1	o(t	o(t	NOUN
ejpam-6387	272	2	1	1	NUM
ejpam-6387	272	3	2	2	NUM
ejpam-6387	272	4	)	)	PUNCT
ejpam-6387	272	5	.	.	PUNCT
ejpam-6387	273	1	one	one	PRON
ejpam-6387	273	2	can	can	AUX
ejpam-6387	273	3	show	show	VERB
ejpam-6387	273	4	the	the	DET
ejpam-6387	273	5	connection	connection	NOUN
ejpam-6387	273	6	between	between	ADP
ejpam-6387	273	7	σ	σ	PROPN
ejpam-6387	273	8	and	and	CCONJ
ejpam-6387	273	9	0	0	NUM
ejpam-6387	273	10	<	<	X
ejpam-6387	273	11	c	c	X
ejpam-6387	273	12	<	<	X
ejpam-6387	273	13	2	2	NUM
ejpam-6387	273	14	by	by	ADP
ejpam-6387	273	15	the	the	DET
ejpam-6387	273	16	following	follow	VERB
ejpam-6387	273	17	table	table	NOUN
ejpam-6387	273	18	:	:	PUNCT
ejpam-6387	273	19	table	table	NOUN
ejpam-6387	273	20	2	2	NUM
ejpam-6387	273	21	:	:	PUNCT
ejpam-6387	273	22	the	the	DET
ejpam-6387	273	23	effect	effect	NOUN
ejpam-6387	273	24	of	of	ADP
ejpam-6387	273	25	c	c	PROPN
ejpam-6387	273	26	on	on	ADP
ejpam-6387	273	27	σ	σ	PROPN
ejpam-6387	273	28	c	c	PROPN
ejpam-6387	274	1	ζ0(σ	ζ0(σ	PROPN
ejpam-6387	274	2	+	+	CCONJ
ejpam-6387	274	3	it	it	PRON
ejpam-6387	274	4	)	)	PUNCT
ejpam-6387	274	5	σ	σ	PROPN
ejpam-6387	274	6	1	1	NUM
ejpam-6387	274	7	10	10	NUM
ejpam-6387	274	8	o(t0.1	o(t0.1	NOUN
ejpam-6387	274	9	)	)	PUNCT
ejpam-6387	274	10	≥	≥	NOUN
ejpam-6387	274	11	1−	1−	NUM
ejpam-6387	274	12	(	(	PUNCT
ejpam-6387	274	13	log	log	VERB
ejpam-6387	274	14	1	1	NUM
ejpam-6387	274	15	10	10	NUM
ejpam-6387	274	16	+	+	CCONJ
ejpam-6387	274	17	1	1	NUM
ejpam-6387	274	18	3	3	NUM
ejpam-6387	274	19	log	log	NOUN
ejpam-6387	274	20	log	log	NOUN
ejpam-6387	274	21	t	t	PROPN
ejpam-6387	274	22	100	100	NUM
ejpam-6387	274	23	log	log	NOUN
ejpam-6387	274	24	t	t	PROPN
ejpam-6387	274	25	)	)	PUNCT
ejpam-6387	274	26	2	2	NUM
ejpam-6387	274	27	3	3	NUM
ejpam-6387	274	28	1	1	NUM
ejpam-6387	274	29	2	2	NUM
ejpam-6387	274	30	o(t0.5	o(t0.5	NOUN
ejpam-6387	274	31	)	)	PUNCT
ejpam-6387	274	32	≥	≥	NOUN
ejpam-6387	274	33	1−	1−	NUM
ejpam-6387	274	34	(	(	PUNCT
ejpam-6387	274	35	log	log	VERB
ejpam-6387	274	36	1	1	NUM
ejpam-6387	274	37	2	2	NUM
ejpam-6387	274	38	+	+	CCONJ
ejpam-6387	274	39	1	1	NUM
ejpam-6387	274	40	3	3	NUM
ejpam-6387	274	41	log	log	NOUN
ejpam-6387	274	42	log	log	NOUN
ejpam-6387	274	43	t	t	PROPN
ejpam-6387	274	44	100	100	NUM
ejpam-6387	274	45	log	log	NOUN
ejpam-6387	274	46	t	t	PROPN
ejpam-6387	274	47	)	)	PUNCT
ejpam-6387	274	48	2	2	NUM
ejpam-6387	274	49	3	3	NUM
ejpam-6387	274	50	9	9	NUM
ejpam-6387	274	51	10	10	NUM
ejpam-6387	274	52	o(t0.9	o(t0.9	NOUN
ejpam-6387	274	53	)	)	PUNCT
ejpam-6387	274	54	≥	≥	NOUN
ejpam-6387	274	55	1−	1−	NUM
ejpam-6387	275	1	(	(	PUNCT
ejpam-6387	275	2	log	log	VERB
ejpam-6387	275	3	9	9	NUM
ejpam-6387	275	4	10	10	NUM
ejpam-6387	275	5	+	+	CCONJ
ejpam-6387	275	6	1	1	NUM
ejpam-6387	275	7	3	3	NUM
ejpam-6387	275	8	log	log	NOUN
ejpam-6387	275	9	log	log	NOUN
ejpam-6387	275	10	t	t	PROPN
ejpam-6387	275	11	100	100	NUM
ejpam-6387	275	12	log	log	NOUN
ejpam-6387	275	13	t	t	PROPN
ejpam-6387	275	14	)	)	PUNCT
ejpam-6387	275	15	2	2	NUM
ejpam-6387	275	16	3	3	NUM
ejpam-6387	275	17	3	3	NUM
ejpam-6387	275	18	2	2	NUM
ejpam-6387	275	19	o(t	o(t	NOUN
ejpam-6387	275	20	3	3	NUM
ejpam-6387	275	21	2	2	NUM
ejpam-6387	275	22	)	)	PUNCT
ejpam-6387	275	23	≥	≥	NOUN
ejpam-6387	275	24	1−	1−	NUM
ejpam-6387	275	25	(	(	PUNCT
ejpam-6387	275	26	log	log	VERB
ejpam-6387	275	27	3	3	NUM
ejpam-6387	275	28	2	2	NUM
ejpam-6387	275	29	+	+	CCONJ
ejpam-6387	275	30	1	1	NUM
ejpam-6387	275	31	3	3	NUM
ejpam-6387	275	32	log	log	NOUN
ejpam-6387	275	33	log	log	NOUN
ejpam-6387	275	34	t	t	PROPN
ejpam-6387	275	35	100	100	NUM
ejpam-6387	275	36	log	log	NOUN
ejpam-6387	275	37	t	t	PROPN
ejpam-6387	275	38	)	)	PUNCT
ejpam-6387	275	39	2	2	NUM
ejpam-6387	275	40	3	3	NUM
ejpam-6387	275	41	from	from	ADP
ejpam-6387	275	42	the	the	DET
ejpam-6387	275	43	above	above	ADJ
ejpam-6387	275	44	table	table	NOUN
ejpam-6387	275	45	one	one	PRON
ejpam-6387	275	46	can	can	AUX
ejpam-6387	275	47	see	see	VERB
ejpam-6387	275	48	that	that	SCONJ
ejpam-6387	275	49	when	when	SCONJ
ejpam-6387	275	50	c	c	NOUN
ejpam-6387	275	51	get	get	VERB
ejpam-6387	275	52	closer	close	ADJ
ejpam-6387	275	53	to	to	ADP
ejpam-6387	275	54	1,the	1,the	NUM
ejpam-6387	275	55	region	region	NOUN
ejpam-6387	275	56	of	of	ADP
ejpam-6387	275	57	σ	σ	PROPN
ejpam-6387	275	58	get	get	VERB
ejpam-6387	275	59	smaller	small	ADJ
ejpam-6387	275	60	and	and	CCONJ
ejpam-6387	275	61	also	also	ADV
ejpam-6387	275	62	when	when	SCONJ
ejpam-6387	275	63	1	1	NUM
ejpam-6387	275	64	<	<	X
ejpam-6387	275	65	c	c	X
ejpam-6387	275	66	<	<	X
ejpam-6387	275	67	2	2	NUM
ejpam-6387	275	68	,	,	PUNCT
ejpam-6387	275	69	the	the	DET
ejpam-6387	275	70	region	region	NOUN
ejpam-6387	275	71	of	of	ADP
ejpam-6387	275	72	σ	σ	PROPN
ejpam-6387	275	73	get	get	VERB
ejpam-6387	275	74	smaller	small	ADJ
ejpam-6387	275	75	and	and	CCONJ
ejpam-6387	275	76	smaller	small	ADJ
ejpam-6387	275	77	.	.	PUNCT
ejpam-6387	276	1	6	6	X
ejpam-6387	276	2	.	.	X
ejpam-6387	276	3	conclusion	conclusion	NOUN
ejpam-6387	276	4	in	in	ADP
ejpam-6387	276	5	conclusion	conclusion	NOUN
ejpam-6387	276	6	,	,	PUNCT
ejpam-6387	276	7	the	the	DET
ejpam-6387	276	8	purpose	purpose	NOUN
ejpam-6387	276	9	of	of	ADP
ejpam-6387	276	10	this	this	DET
ejpam-6387	276	11	work	work	NOUN
ejpam-6387	276	12	was	be	AUX
ejpam-6387	276	13	to	to	PART
ejpam-6387	276	14	concentrate	concentrate	VERB
ejpam-6387	276	15	on	on	ADP
ejpam-6387	276	16	the	the	DET
ejpam-6387	276	17	impact	impact	NOUN
ejpam-6387	276	18	of	of	ADP
ejpam-6387	276	19	the	the	DET
ejpam-6387	276	20	order	order	NOUN
ejpam-6387	276	21	of	of	ADP
ejpam-6387	276	22	beurling	beurle	VERB
ejpam-6387	276	23	zeta	zeta	PROPN
ejpam-6387	276	24	function	function	NOUN
ejpam-6387	276	25	ζp(s	ζp(s	NOUN
ejpam-6387	276	26	)	)	PUNCT
ejpam-6387	276	27	on	on	ADP
ejpam-6387	276	28	the	the	DET
ejpam-6387	276	29	size	size	NOUN
ejpam-6387	276	30	of	of	ADP
ejpam-6387	276	31	error	error	NOUN
ejpam-6387	276	32	term	term	NOUN
ejpam-6387	276	33	of	of	ADP
ejpam-6387	276	34	beurling	beurle	VERB
ejpam-6387	276	35	integer	integer	NOUN
ejpam-6387	276	36	counting	counting	NOUN
ejpam-6387	276	37	function	function	NOUN
ejpam-6387	276	38	np(x	np(x	NUM
ejpam-6387	276	39	)	)	PUNCT
ejpam-6387	276	40	.	.	PUNCT
ejpam-6387	277	1	in	in	ADP
ejpam-6387	277	2	particular	particular	ADJ
ejpam-6387	277	3	,	,	PUNCT
ejpam-6387	277	4	we	we	PRON
ejpam-6387	277	5	discovered	discover	VERB
ejpam-6387	277	6	by	by	ADP
ejpam-6387	277	7	changing	change	VERB
ejpam-6387	277	8	the	the	DET
ejpam-6387	277	9	interval	interval	NOUN
ejpam-6387	277	10	of	of	ADP
ejpam-6387	277	11	constant	constant	ADJ
ejpam-6387	277	12	c	c	NOUN
ejpam-6387	277	13	in	in	ADP
ejpam-6387	277	14	theorem	theorem	NOUN
ejpam-6387	277	15	(	(	PUNCT
ejpam-6387	277	16	1	1	NUM
ejpam-6387	277	17	)	)	PUNCT
ejpam-6387	277	18	,	,	PUNCT
ejpam-6387	277	19	different	different	ADJ
ejpam-6387	277	20	results	result	NOUN
ejpam-6387	277	21	has	have	AUX
ejpam-6387	277	22	been	be	AUX
ejpam-6387	277	23	achieved	achieve	VERB
ejpam-6387	277	24	.	.	PUNCT
ejpam-6387	278	1	first	first	ADV
ejpam-6387	278	2	,	,	PUNCT
ejpam-6387	278	3	when	when	SCONJ
ejpam-6387	278	4	constant	constant	ADJ
ejpam-6387	278	5	0	0	PUNCT
ejpam-6387	278	6	<	<	X
ejpam-6387	278	7	c	c	X
ejpam-6387	278	8	<	<	X
ejpam-6387	278	9	1	1	NUM
ejpam-6387	278	10	the	the	DET
ejpam-6387	278	11	error	error	NOUN
ejpam-6387	278	12	term	term	NOUN
ejpam-6387	278	13	of	of	ADP
ejpam-6387	278	14	np(x	np(x	NOUN
ejpam-6387	278	15	)	)	PUNCT
ejpam-6387	278	16	has	have	VERB
ejpam-6387	278	17	different	different	ADJ
ejpam-6387	278	18	explanation	explanation	NOUN
ejpam-6387	278	19	.	.	PUNCT
ejpam-6387	279	1	second	second	ADJ
ejpam-6387	279	2	if	if	SCONJ
ejpam-6387	279	3	constant	constant	ADJ
ejpam-6387	279	4	1	1	NUM
ejpam-6387	279	5	<	<	X
ejpam-6387	279	6	c	c	X
ejpam-6387	279	7	<	<	X
ejpam-6387	279	8	2	2	NUM
ejpam-6387	279	9	,	,	PUNCT
ejpam-6387	279	10	then	then	ADV
ejpam-6387	279	11	the	the	DET
ejpam-6387	279	12	error	error	NOUN
ejpam-6387	279	13	term	term	NOUN
ejpam-6387	279	14	of	of	ADP
ejpam-6387	279	15	np(x	np(x	NOUN
ejpam-6387	279	16	)	)	PUNCT
ejpam-6387	279	17	is	be	AUX
ejpam-6387	279	18	big	big	ADJ
ejpam-6387	279	19	as	as	SCONJ
ejpam-6387	279	20	it	it	PRON
ejpam-6387	279	21	shown	show	VERB
ejpam-6387	279	22	in	in	ADP
ejpam-6387	279	23	section	section	NOUN
ejpam-6387	279	24	(	(	PUNCT
ejpam-6387	279	25	4	4	NUM
ejpam-6387	279	26	)	)	PUNCT
ejpam-6387	279	27	.	.	PUNCT
ejpam-6387	280	1	but	but	CCONJ
ejpam-6387	280	2	then	then	ADV
ejpam-6387	280	3	by	by	ADP
ejpam-6387	280	4	adding	add	VERB
ejpam-6387	280	5	some	some	DET
ejpam-6387	280	6	condition	condition	NOUN
ejpam-6387	280	7	to	to	ADP
ejpam-6387	280	8	theorem	theorem	NOUN
ejpam-6387	280	9	(	(	PUNCT
ejpam-6387	280	10	1	1	NUM
ejpam-6387	280	11	)	)	PUNCT
ejpam-6387	280	12	,	,	PUNCT
ejpam-6387	280	13	the	the	DET
ejpam-6387	280	14	error	error	NOUN
ejpam-6387	280	15	term	term	NOUN
ejpam-6387	280	16	of	of	ADP
ejpam-6387	280	17	np(x	np(x	NOUN
ejpam-6387	280	18	)	)	PUNCT
ejpam-6387	280	19	became	become	VERB
ejpam-6387	280	20	smaller	small	ADJ
ejpam-6387	280	21	as	as	SCONJ
ejpam-6387	280	22	it	it	PRON
ejpam-6387	280	23	shown	show	VERB
ejpam-6387	280	24	in	in	ADP
ejpam-6387	280	25	lemma	lemma	PROPN
ejpam-6387	280	26	(	(	PUNCT
ejpam-6387	280	27	4).further	4).further	ADV
ejpam-6387	280	28	more	more	ADJ
ejpam-6387	280	29	,	,	PUNCT
ejpam-6387	280	30	when	when	SCONJ
ejpam-6387	280	31	constant	constant	ADJ
ejpam-6387	280	32	c	c	NOUN
ejpam-6387	280	33	=	=	SYM
ejpam-6387	280	34	1	1	NUM
ejpam-6387	280	35	and	and	CCONJ
ejpam-6387	280	36	c	c	NOUN
ejpam-6387	280	37	≥	≥	NUM
ejpam-6387	280	38	2	2	NUM
ejpam-6387	280	39	,	,	PUNCT
ejpam-6387	280	40	np(x	np(x	NUM
ejpam-6387	280	41	)	)	PUNCT
ejpam-6387	280	42	diverges	diverge	NOUN
ejpam-6387	280	43	.	.	PUNCT
ejpam-6387	281	1	in	in	ADP
ejpam-6387	281	2	addition	addition	NOUN
ejpam-6387	281	3	,	,	PUNCT
ejpam-6387	281	4	this	this	DET
ejpam-6387	281	5	work	work	NOUN
ejpam-6387	281	6	also	also	ADV
ejpam-6387	281	7	focused	focus	VERB
ejpam-6387	281	8	on	on	ADP
ejpam-6387	281	9	the	the	DET
ejpam-6387	281	10	connection	connection	NOUN
ejpam-6387	281	11	between	between	ADP
ejpam-6387	281	12	constant	constant	ADJ
ejpam-6387	281	13	c	c	NOUN
ejpam-6387	281	14	in	in	ADP
ejpam-6387	281	15	the	the	DET
ejpam-6387	281	16	order	order	NOUN
ejpam-6387	281	17	of	of	ADP
ejpam-6387	281	18	ζp(s	ζp(s	NOUN
ejpam-6387	281	19	)	)	PUNCT
ejpam-6387	281	20	and	and	CCONJ
ejpam-6387	281	21	the	the	DET
ejpam-6387	281	22	real	real	ADJ
ejpam-6387	281	23	part	part	NOUN
ejpam-6387	281	24	σ	σ	NOUN
ejpam-6387	281	25	of	of	ADP
ejpam-6387	281	26	ζp(s	ζp(s	NOUN
ejpam-6387	281	27	)	)	PUNCT
ejpam-6387	281	28	.	.	PUNCT
ejpam-6387	282	1	z.	z.	PROPN
ejpam-6387	282	2	m.	m.	PROPN
ejpam-6387	282	3	amen	amen	INTJ
ejpam-6387	282	4	,	,	PUNCT
ejpam-6387	282	5	f.	f.	PROPN
ejpam-6387	282	6	a.	a.	PROPN
ejpam-6387	282	7	al	al	PROPN
ejpam-6387	282	8	-	-	PUNCT
ejpam-6387	282	9	maamori	maamori	PROPN
ejpam-6387	282	10	,	,	PUNCT
ejpam-6387	282	11	m.	m.	NOUN
ejpam-6387	282	12	f.	f.	PROPN
ejpam-6387	282	13	hama	hama	PROPN
ejpam-6387	282	14	/	/	SYM
ejpam-6387	282	15	eur	eur	PROPN
ejpam-6387	282	16	.	.	PUNCT
ejpam-6387	283	1	j.	j.	PROPN
ejpam-6387	283	2	pure	pure	PROPN
ejpam-6387	283	3	appl	appl	PROPN
ejpam-6387	283	4	.	.	PROPN
ejpam-6387	283	5	math	math	PROPN
ejpam-6387	283	6	,	,	PUNCT
ejpam-6387	283	7	18	18	NUM
ejpam-6387	283	8	(	(	PUNCT
ejpam-6387	283	9	4	4	NUM
ejpam-6387	283	10	)	)	PUNCT
ejpam-6387	283	11	(	(	PUNCT
ejpam-6387	283	12	2025	2025	NUM
ejpam-6387	283	13	)	)	PUNCT
ejpam-6387	283	14	,	,	PUNCT
ejpam-6387	283	15	6387	6387	NUM
ejpam-6387	283	16	15	15	NUM
ejpam-6387	283	17	of	of	ADP
ejpam-6387	283	18	15	15	NUM
ejpam-6387	283	19	references	reference	NOUN
ejpam-6387	283	20	[	[	X
ejpam-6387	283	21	1	1	NUM
ejpam-6387	283	22	]	]	PUNCT
ejpam-6387	283	23	t.	t.	PROPN
ejpam-6387	283	24	m.	m.	NOUN
ejpam-6387	283	25	apostol	apostol	PROPN
ejpam-6387	283	26	.	.	PUNCT
ejpam-6387	284	1	introduction	introduction	NOUN
ejpam-6387	284	2	to	to	ADP
ejpam-6387	284	3	analytic	analytic	ADJ
ejpam-6387	284	4	number	number	NOUN
ejpam-6387	284	5	theory	theory	NOUN
ejpam-6387	284	6	.	.	PUNCT
ejpam-6387	285	1	springer	springer	NOUN
ejpam-6387	285	2	,	,	PUNCT
ejpam-6387	285	3	1976	1976	NUM
ejpam-6387	285	4	.	.	PUNCT
ejpam-6387	286	1	[	[	X
ejpam-6387	286	2	2	2	NUM
ejpam-6387	286	3	]	]	PUNCT
ejpam-6387	286	4	a.	a.	NOUN
ejpam-6387	286	5	beurling	beurling	NOUN
ejpam-6387	286	6	.	.	PUNCT
ejpam-6387	287	1	analyse	analyse	PROPN
ejpam-6387	287	2	de	de	PROPN
ejpam-6387	287	3	la	la	PROPN
ejpam-6387	287	4	loi	loi	PROPN
ejpam-6387	287	5	asymptotique	asymptotique	PROPN
ejpam-6387	287	6	de	de	X
ejpam-6387	287	7	la	la	X
ejpam-6387	287	8	distribution	distribution	NOUN
ejpam-6387	287	9	des	des	X
ejpam-6387	287	10	nombres	nombre	NOUN
ejpam-6387	287	11	premiers	premiers	PROPN
ejpam-6387	287	12	généralisés	généralisés	NOUN
ejpam-6387	287	13	.	.	PUNCT
ejpam-6387	288	1	acta	acta	PROPN
ejpam-6387	288	2	mathematica	mathematica	PROPN
ejpam-6387	288	3	,	,	PUNCT
ejpam-6387	288	4	68:255–291	68:255–291	PROPN
ejpam-6387	288	5	,	,	PUNCT
ejpam-6387	288	6	1937	1937	NUM
ejpam-6387	288	7	.	.	PUNCT
ejpam-6387	289	1	[	[	X
ejpam-6387	289	2	3	3	X
ejpam-6387	289	3	]	]	X
ejpam-6387	289	4	h.	h.	PROPN
ejpam-6387	289	5	g.	g.	PROPN
ejpam-6387	289	6	diamond	diamond	PROPN
ejpam-6387	289	7	.	.	PUNCT
ejpam-6387	290	1	asymptotic	asymptotic	ADJ
ejpam-6387	290	2	distribution	distribution	NOUN
ejpam-6387	290	3	of	of	ADP
ejpam-6387	290	4	beurling	beurle	VERB
ejpam-6387	290	5	’s	’s	PART
ejpam-6387	290	6	generalised	generalise	VERB
ejpam-6387	290	7	integers	integer	NOUN
ejpam-6387	290	8	.	.	PUNCT
ejpam-6387	291	1	illinois	illinois	PROPN
ejpam-6387	291	2	journal	journal	PROPN
ejpam-6387	291	3	of	of	ADP
ejpam-6387	291	4	mathematics	mathematic	NOUN
ejpam-6387	291	5	,	,	PUNCT
ejpam-6387	291	6	14:12–28	14:12–28	NUM
ejpam-6387	291	7	,	,	PUNCT
ejpam-6387	291	8	1970	1970	NUM
ejpam-6387	291	9	.	.	PUNCT
ejpam-6387	292	1	[	[	X
ejpam-6387	292	2	4	4	X
ejpam-6387	292	3	]	]	X
ejpam-6387	292	4	p.	p.	NOUN
ejpam-6387	292	5	t.	t.	PROPN
ejpam-6387	292	6	bateman	bateman	PROPN
ejpam-6387	292	7	and	and	CCONJ
ejpam-6387	292	8	h.	h.	PROPN
ejpam-6387	292	9	g.	g.	PROPN
ejpam-6387	292	10	diamond	diamond	PROPN
ejpam-6387	292	11	.	.	PUNCT
ejpam-6387	293	1	asymptotic	asymptotic	ADJ
ejpam-6387	293	2	distribution	distribution	NOUN
ejpam-6387	293	3	of	of	ADP
ejpam-6387	293	4	beurling	beurle	VERB
ejpam-6387	293	5	’s	’s	PART
ejpam-6387	293	6	generalised	generalise	VERB
ejpam-6387	293	7	prime	prime	ADJ
ejpam-6387	293	8	numbers	number	NOUN
ejpam-6387	293	9	.	.	PUNCT
ejpam-6387	294	1	in	in	ADP
ejpam-6387	294	2	studies	study	NOUN
ejpam-6387	294	3	in	in	ADP
ejpam-6387	294	4	number	number	NOUN
ejpam-6387	294	5	theory	theory	NOUN
ejpam-6387	294	6	,	,	PUNCT
ejpam-6387	294	7	pages	page	NOUN
ejpam-6387	294	8	152–212	152–212	NUM
ejpam-6387	294	9	.	.	PUNCT
ejpam-6387	295	1	mathematical	mathematical	ADJ
ejpam-6387	295	2	association	association	PROPN
ejpam-6387	295	3	of	of	ADP
ejpam-6387	295	4	america	america	PROPN
ejpam-6387	295	5	,	,	PUNCT
ejpam-6387	295	6	1969	1969	NUM
ejpam-6387	295	7	.	.	PUNCT
ejpam-6387	296	1	[	[	X
ejpam-6387	296	2	5	5	X
ejpam-6387	296	3	]	]	PUNCT
ejpam-6387	296	4	h.	h.	NOUN
ejpam-6387	296	5	diamond	diamond	PROPN
ejpam-6387	296	6	.	.	PUNCT
ejpam-6387	297	1	the	the	DET
ejpam-6387	297	2	prime	prime	ADJ
ejpam-6387	297	3	number	number	NOUN
ejpam-6387	297	4	theorem	theorem	VERB
ejpam-6387	297	5	for	for	ADP
ejpam-6387	297	6	beurling	beurle	VERB
ejpam-6387	297	7	’s	’s	PART
ejpam-6387	297	8	generalised	generalise	VERB
ejpam-6387	297	9	numbers	number	NOUN
ejpam-6387	297	10	.	.	PUNCT
ejpam-6387	298	1	journal	journal	NOUN
ejpam-6387	298	2	of	of	ADP
ejpam-6387	298	3	number	number	NOUN
ejpam-6387	298	4	theory	theory	NOUN
ejpam-6387	298	5	,	,	PUNCT
ejpam-6387	298	6	1:200–207	1:200–207	NOUN
ejpam-6387	298	7	,	,	PUNCT
ejpam-6387	298	8	1969	1969	NUM
ejpam-6387	298	9	.	.	PUNCT
ejpam-6387	299	1	[	[	X
ejpam-6387	299	2	6	6	NUM
ejpam-6387	299	3	]	]	PUNCT
ejpam-6387	299	4	h.	h.	PROPN
ejpam-6387	299	5	g.	g.	PROPN
ejpam-6387	299	6	diamond	diamond	PROPN
ejpam-6387	299	7	.	.	PUNCT
ejpam-6387	300	1	a	a	DET
ejpam-6387	300	2	set	set	NOUN
ejpam-6387	300	3	of	of	ADP
ejpam-6387	300	4	generalised	generalise	VERB
ejpam-6387	300	5	numbers	number	NOUN
ejpam-6387	300	6	showing	show	VERB
ejpam-6387	300	7	beurling	beurling	NOUN
ejpam-6387	300	8	’s	’s	PART
ejpam-6387	300	9	theorem	theorem	NOUN
ejpam-6387	300	10	to	to	PART
ejpam-6387	300	11	be	be	AUX
ejpam-6387	300	12	sharp	sharp	ADJ
ejpam-6387	300	13	.	.	PUNCT
ejpam-6387	301	1	illinois	illinois	PROPN
ejpam-6387	301	2	journal	journal	PROPN
ejpam-6387	301	3	of	of	ADP
ejpam-6387	301	4	mathematics	mathematics	PROPN
ejpam-6387	301	5	,	,	PUNCT
ejpam-6387	301	6	14:29–34	14:29–34	NUM
ejpam-6387	301	7	,	,	PUNCT
ejpam-6387	301	8	1970	1970	NUM
ejpam-6387	301	9	.	.	PUNCT
ejpam-6387	302	1	[	[	X
ejpam-6387	302	2	7	7	X
ejpam-6387	302	3	]	]	X
ejpam-6387	302	4	h.	h.	NOUN
ejpam-6387	302	5	diamond	diamond	PROPN
ejpam-6387	302	6	.	.	PUNCT
ejpam-6387	303	1	when	when	SCONJ
ejpam-6387	303	2	do	do	AUX
ejpam-6387	303	3	beurling	beurle	VERB
ejpam-6387	303	4	’s	’s	PART
ejpam-6387	303	5	generalised	generalise	VERB
ejpam-6387	303	6	integers	integer	NOUN
ejpam-6387	303	7	have	have	VERB
ejpam-6387	303	8	density	density	NOUN
ejpam-6387	303	9	?	?	PUNCT
ejpam-6387	304	1	journal	journal	PROPN
ejpam-6387	304	2	für	für	PROPN
ejpam-6387	304	3	die	die	VERB
ejpam-6387	304	4	reine	reine	PROPN
ejpam-6387	304	5	und	und	PROPN
ejpam-6387	304	6	angewandte	angewandte	PROPN
ejpam-6387	304	7	mathematik	mathematik	PROPN
ejpam-6387	304	8	,	,	PUNCT
ejpam-6387	304	9	295:22–39	295:22–39	PROPN
ejpam-6387	304	10	,	,	PUNCT
ejpam-6387	304	11	1977	1977	NUM
ejpam-6387	304	12	.	.	PUNCT
ejpam-6387	305	1	[	[	X
ejpam-6387	305	2	8	8	NUM
ejpam-6387	305	3	]	]	PUNCT
ejpam-6387	305	4	p.	p.	NOUN
ejpam-6387	305	5	malliavin	malliavin	PROPN
ejpam-6387	305	6	.	.	PUNCT
ejpam-6387	306	1	sur	sur	PROPN
ejpam-6387	306	2	le	le	X
ejpam-6387	306	3	reste	reste	PROPN
ejpam-6387	306	4	de	de	X
ejpam-6387	306	5	la	la	PROPN
ejpam-6387	306	6	loi	loi	PROPN
ejpam-6387	306	7	asymptotique	asymptotique	PROPN
ejpam-6387	306	8	de	de	PROPN
ejpam-6387	306	9	répartition	répartition	PROPN
ejpam-6387	306	10	des	des	PROPN
ejpam-6387	306	11	nombres	nombres	PROPN
ejpam-6387	306	12	premiers	premiers	PROPN
ejpam-6387	306	13	généralisés	généralisés	PROPN
ejpam-6387	306	14	de	de	ADP
ejpam-6387	306	15	beurling	beurling	PROPN
ejpam-6387	306	16	.	.	PUNCT
ejpam-6387	307	1	acta	acta	PROPN
ejpam-6387	307	2	mathematica	mathematica	PROPN
ejpam-6387	307	3	,	,	PUNCT
ejpam-6387	307	4	106:281–298	106:281–298	NUM
ejpam-6387	307	5	,	,	PUNCT
ejpam-6387	307	6	1961	1961	NUM
ejpam-6387	307	7	.	.	PUNCT
ejpam-6387	308	1	[	[	X
ejpam-6387	308	2	9	9	NUM
ejpam-6387	308	3	]	]	X
ejpam-6387	308	4	b.	b.	PROPN
ejpam-6387	308	5	nyman	nyman	PROPN
ejpam-6387	308	6	.	.	PUNCT
ejpam-6387	309	1	a	a	DET
ejpam-6387	309	2	general	general	ADJ
ejpam-6387	309	3	prime	prime	ADJ
ejpam-6387	309	4	number	number	NOUN
ejpam-6387	309	5	theorem	theorem	VERB
ejpam-6387	309	6	.	.	PUNCT
ejpam-6387	310	1	acta	acta	PROPN
ejpam-6387	310	2	mathematica	mathematica	PROPN
ejpam-6387	310	3	,	,	PUNCT
ejpam-6387	310	4	81:299–307	81:299–307	PROPN
ejpam-6387	310	5	,	,	PUNCT
ejpam-6387	310	6	1949	1949	NUM
ejpam-6387	310	7	.	.	PUNCT
ejpam-6387	311	1	[	[	X
ejpam-6387	311	2	10	10	NUM
ejpam-6387	311	3	]	]	X
ejpam-6387	311	4	r.	r.	PROPN
ejpam-6387	311	5	s.	s.	PROPN
ejpam-6387	311	6	hall	hall	PROPN
ejpam-6387	311	7	.	.	PUNCT
ejpam-6387	312	1	theorems	theorem	NOUN
ejpam-6387	312	2	about	about	ADP
ejpam-6387	312	3	beurling	beurle	VERB
ejpam-6387	312	4	generalised	generalise	VERB
ejpam-6387	312	5	prime	prime	NOUN
ejpam-6387	312	6	and	and	CCONJ
ejpam-6387	312	7	associated	associated	ADJ
ejpam-6387	312	8	zeta	zeta	NOUN
ejpam-6387	312	9	function	function	NOUN
ejpam-6387	312	10	.	.	PUNCT
ejpam-6387	313	1	phd	phd	NOUN
ejpam-6387	313	2	thesis	thesis	PROPN
ejpam-6387	313	3	,	,	PUNCT
ejpam-6387	313	4	university	university	PROPN
ejpam-6387	313	5	of	of	ADP
ejpam-6387	313	6	illinois	illinois	PROPN
ejpam-6387	313	7	,	,	PUNCT
ejpam-6387	313	8	usa	usa	PROPN
ejpam-6387	313	9	,	,	PUNCT
ejpam-6387	313	10	1967	1967	NUM
ejpam-6387	313	11	.	.	PUNCT
ejpam-6387	314	1	[	[	X
ejpam-6387	314	2	11	11	NUM
ejpam-6387	314	3	]	]	PUNCT
ejpam-6387	314	4	j.	j.	PROPN
ejpam-6387	314	5	p.	p.	PROPN
ejpam-6387	314	6	kahane	kahane	PROPN
ejpam-6387	314	7	.	.	PUNCT
ejpam-6387	315	1	sur	sur	PROPN
ejpam-6387	315	2	les	les	PROPN
ejpam-6387	315	3	nombres	nombres	PROPN
ejpam-6387	315	4	premiers	premiers	PROPN
ejpam-6387	315	5	généralisés	généralisés	PROPN
ejpam-6387	315	6	de	de	X
ejpam-6387	315	7	beurling	beurling	PROPN
ejpam-6387	315	8	.	.	PUNCT
ejpam-6387	316	1	journal	journal	PROPN
ejpam-6387	316	2	de	de	PROPN
ejpam-6387	316	3	théorie	théorie	PROPN
ejpam-6387	316	4	des	des	PROPN
ejpam-6387	316	5	nombres	nombres	PROPN
ejpam-6387	316	6	de	de	X
ejpam-6387	316	7	bordeaux	bordeaux	PROPN
ejpam-6387	316	8	,	,	PUNCT
ejpam-6387	316	9	9:251–266	9:251–266	NOUN
ejpam-6387	316	10	,	,	PUNCT
ejpam-6387	316	11	1997	1997	NUM
ejpam-6387	316	12	.	.	PUNCT
ejpam-6387	317	1	[	[	X
ejpam-6387	317	2	12	12	NUM
ejpam-6387	317	3	]	]	PUNCT
ejpam-6387	317	4	j.	j.	PROPN
ejpam-6387	317	5	c.	c.	PROPN
ejpam-6387	317	6	lagarias	lagarias	PROPN
ejpam-6387	317	7	.	.	PUNCT
ejpam-6387	318	1	beurling	beurle	VERB
ejpam-6387	318	2	generalised	generalise	VERB
ejpam-6387	318	3	integers	integer	NOUN
ejpam-6387	318	4	with	with	ADP
ejpam-6387	318	5	the	the	DET
ejpam-6387	318	6	delone	delone	NOUN
ejpam-6387	318	7	property	property	NOUN
ejpam-6387	318	8	.	.	PUNCT
ejpam-6387	319	1	forum	forum	PROPN
ejpam-6387	319	2	mathematicum	mathematicum	PROPN
ejpam-6387	319	3	,	,	PUNCT
ejpam-6387	319	4	11:295–312	11:295–312	NUM
ejpam-6387	319	5	,	,	PUNCT
ejpam-6387	319	6	1999	1999	NUM
ejpam-6387	319	7	.	.	PUNCT
ejpam-6387	320	1	[	[	X
ejpam-6387	320	2	13	13	NUM
ejpam-6387	320	3	]	]	PUNCT
ejpam-6387	320	4	w.	w.	PROPN
ejpam-6387	320	5	zhang	zhang	PROPN
ejpam-6387	320	6	.	.	PUNCT
ejpam-6387	321	1	beurling	beurle	VERB
ejpam-6387	321	2	primes	prime	NOUN
ejpam-6387	321	3	with	with	ADP
ejpam-6387	321	4	rh	rh	PROPN
ejpam-6387	321	5	,	,	PUNCT
ejpam-6387	321	6	beurling	beurle	VERB
ejpam-6387	321	7	primes	prime	NOUN
ejpam-6387	321	8	with	with	ADP
ejpam-6387	321	9	large	large	ADJ
ejpam-6387	321	10	oscillation	oscillation	NOUN
ejpam-6387	321	11	.	.	PUNCT
ejpam-6387	322	1	mathematische	mathematische	PROPN
ejpam-6387	322	2	annalen	annalen	PROPN
ejpam-6387	322	3	,	,	PUNCT
ejpam-6387	322	4	337:671–704	337:671–704	NUM
ejpam-6387	322	5	,	,	PUNCT
ejpam-6387	322	6	2007	2007	NUM
ejpam-6387	322	7	.	.	PUNCT
ejpam-6387	323	1	[	[	X
ejpam-6387	323	2	14	14	NUM
ejpam-6387	323	3	]	]	X
ejpam-6387	323	4	c.	c.	PROPN
ejpam-6387	323	5	cesarano	cesarano	PROPN
ejpam-6387	323	6	,	,	PUNCT
ejpam-6387	323	7	w.	w.	PROPN
ejpam-6387	323	8	ramirez	ramirez	PROPN
ejpam-6387	323	9	,	,	PUNCT
ejpam-6387	323	10	and	and	CCONJ
ejpam-6387	323	11	s.	s.	PROPN
ejpam-6387	323	12	diaz	diaz	PROPN
ejpam-6387	323	13	.	.	PUNCT
ejpam-6387	324	1	new	new	ADJ
ejpam-6387	324	2	results	result	NOUN
ejpam-6387	324	3	for	for	ADP
ejpam-6387	324	4	degenerated	degenerated	ADJ
ejpam-6387	324	5	generalised	generalise	VERB
ejpam-6387	324	6	apostol	apostol	NOUN
ejpam-6387	324	7	-	-	PUNCT
ejpam-6387	324	8	bernoulli	bernoulli	NOUN
ejpam-6387	324	9	,	,	PUNCT
ejpam-6387	324	10	apostol	apostol	NOUN
ejpam-6387	324	11	-	-	PUNCT
ejpam-6387	324	12	euler	euler	NOUN
ejpam-6387	324	13	and	and	CCONJ
ejpam-6387	324	14	apostol	apostol	NOUN
ejpam-6387	324	15	-	-	PUNCT
ejpam-6387	324	16	genocchi	genocchi	PROPN
ejpam-6387	324	17	polynomials	polynomial	NOUN
ejpam-6387	324	18	.	.	PUNCT
ejpam-6387	325	1	wseas	wseas	VERB
ejpam-6387	325	2	transactions	transaction	NOUN
ejpam-6387	325	3	on	on	ADP
ejpam-6387	325	4	mathematics	mathematic	NOUN
ejpam-6387	325	5	,	,	PUNCT
ejpam-6387	325	6	21:604–608	21:604–608	NUM
ejpam-6387	325	7	,	,	PUNCT
ejpam-6387	325	8	2022	2022	NUM
ejpam-6387	325	9	.	.	PUNCT
ejpam-6387	326	1	[	[	X
ejpam-6387	326	2	15	15	NUM
ejpam-6387	326	3	]	]	X
ejpam-6387	326	4	f.	f.	PROPN
ejpam-6387	326	5	al	al	PROPN
ejpam-6387	326	6	-	-	PUNCT
ejpam-6387	326	7	maamori	maamori	PROPN
ejpam-6387	326	8	.	.	PUNCT
ejpam-6387	327	1	examples	example	NOUN
ejpam-6387	327	2	of	of	ADP
ejpam-6387	327	3	beurling	beurle	VERB
ejpam-6387	327	4	prime	prime	ADJ
ejpam-6387	327	5	systems	system	NOUN
ejpam-6387	327	6	.	.	PUNCT
ejpam-6387	328	1	mathematica	mathematica	PROPN
ejpam-6387	328	2	slovaca	slovaca	PROPN
ejpam-6387	328	3	,	,	PUNCT
ejpam-6387	328	4	67:321–344	67:321–344	PROPN
ejpam-6387	328	5	,	,	PUNCT
ejpam-6387	328	6	2014	2014	NUM
ejpam-6387	328	7	.	.	PUNCT
ejpam-6387	329	1	[	[	X
ejpam-6387	329	2	16	16	NUM
ejpam-6387	329	3	]	]	PUNCT
ejpam-6387	329	4	t.	t.	NOUN
ejpam-6387	329	5	hilberdink	hilberdink	NOUN
ejpam-6387	329	6	and	and	CCONJ
ejpam-6387	329	7	l.	l.	PROPN
ejpam-6387	329	8	lapidus	lapidus	PROPN
ejpam-6387	329	9	.	.	PUNCT
ejpam-6387	330	1	beurling	beurle	VERB
ejpam-6387	330	2	zeta	zeta	PROPN
ejpam-6387	330	3	functions	function	NOUN
ejpam-6387	330	4	,	,	PUNCT
ejpam-6387	330	5	generalised	generalised	ADJ
ejpam-6387	330	6	primes	prime	NOUN
ejpam-6387	330	7	,	,	PUNCT
ejpam-6387	330	8	and	and	CCONJ
ejpam-6387	330	9	fractal	fractal	ADJ
ejpam-6387	330	10	membranes	membrane	NOUN
ejpam-6387	330	11	.	.	PUNCT
ejpam-6387	331	1	acta	acta	PROPN
ejpam-6387	331	2	applicandae	applicandae	PROPN
ejpam-6387	331	3	mathematicae	mathematicae	PROPN
ejpam-6387	331	4	,	,	PUNCT
ejpam-6387	331	5	96:21–48	96:21–48	NUM
ejpam-6387	331	6	,	,	PUNCT
ejpam-6387	331	7	2006	2006	NUM
ejpam-6387	331	8	.	.	PUNCT
ejpam-6387	332	1	[	[	X
ejpam-6387	332	2	17	17	NUM
ejpam-6387	332	3	]	]	PUNCT
ejpam-6387	332	4	a.	a.	NOUN
ejpam-6387	332	5	landau	landau	NOUN
ejpam-6387	332	6	.	.	PUNCT
ejpam-6387	333	1	neuer	neuer	PROPN
ejpam-6387	333	2	beweis	beweis	PROPN
ejpam-6387	333	3	des	des	PROPN
ejpam-6387	333	4	primzahlsatzes	primzahlsatzes	AUX
ejpam-6387	333	5	und	und	VERB
ejpam-6387	333	6	beweis	beweis	PROPN
ejpam-6387	333	7	des	des	PROPN
ejpam-6387	333	8	primidealsatzes	primidealsatzes	PROPN
ejpam-6387	333	9	.	.	PUNCT
ejpam-6387	334	1	mathematische	mathematische	PROPN
ejpam-6387	334	2	annalen	annalen	PROPN
ejpam-6387	334	3	,	,	PUNCT
ejpam-6387	334	4	56:645–670	56:645–670	PROPN
ejpam-6387	334	5	,	,	PUNCT
ejpam-6387	334	6	1903	1903	NUM
ejpam-6387	334	7	.	.	PUNCT
ejpam-6387	335	1	[	[	X
ejpam-6387	335	2	18	18	NUM
ejpam-6387	335	3	]	]	X
ejpam-6387	335	4	h.	h.	PROPN
ejpam-6387	335	5	montgomery	montgomery	PROPN
ejpam-6387	335	6	,	,	PUNCT
ejpam-6387	335	7	h.	h.	PROPN
ejpam-6387	335	8	diamond	diamond	PROPN
ejpam-6387	335	9	,	,	PUNCT
ejpam-6387	335	10	and	and	CCONJ
ejpam-6387	335	11	u.	u.	PROPN
ejpam-6387	335	12	vorhauer	vorhauer	PROPN
ejpam-6387	335	13	.	.	PUNCT
ejpam-6387	336	1	beurling	beurle	VERB
ejpam-6387	336	2	primes	prime	NOUN
ejpam-6387	336	3	with	with	ADP
ejpam-6387	336	4	large	large	ADJ
ejpam-6387	336	5	oscillation	oscillation	NOUN
ejpam-6387	336	6	.	.	PUNCT
ejpam-6387	337	1	mathematische	mathematische	PROPN
ejpam-6387	337	2	annalen	annalen	PROPN
ejpam-6387	337	3	,	,	PUNCT
ejpam-6387	337	4	334:1–36	334:1–36	NUM
ejpam-6387	337	5	,	,	PUNCT
ejpam-6387	337	6	2006	2006	NUM
ejpam-6387	337	7	.	.	PUNCT
ejpam-6387	338	1	[	[	X
ejpam-6387	338	2	19	19	NUM
ejpam-6387	338	3	]	]	PUNCT
ejpam-6387	338	4	e.	e.	PROPN
ejpam-6387	338	5	p.	p.	PROPN
ejpam-6387	338	6	balanzario	balanzario	PROPN
ejpam-6387	338	7	.	.	PUNCT
ejpam-6387	339	1	an	an	DET
ejpam-6387	339	2	example	example	NOUN
ejpam-6387	339	3	in	in	ADP
ejpam-6387	339	4	beurling	beurling	PROPN
ejpam-6387	339	5	’s	’s	PART
ejpam-6387	339	6	theory	theory	NOUN
ejpam-6387	339	7	of	of	ADP
ejpam-6387	339	8	primes	prime	NOUN
ejpam-6387	339	9	.	.	PUNCT
ejpam-6387	340	1	acta	acta	PROPN
ejpam-6387	340	2	mathematica	mathematica	PROPN
ejpam-6387	340	3	,	,	PUNCT
ejpam-6387	340	4	87:121–139	87:121–139	NUM
ejpam-6387	340	5	,	,	PUNCT
ejpam-6387	340	6	1998	1998	NUM
ejpam-6387	340	7	.	.	PUNCT
ejpam-6387	341	1	[	[	X
ejpam-6387	341	2	20	20	NUM
ejpam-6387	341	3	]	]	X
ejpam-6387	341	4	f.	f.	PROPN
ejpam-6387	341	5	al	al	PROPN
ejpam-6387	341	6	-	-	PUNCT
ejpam-6387	341	7	maamori	maamori	PROPN
ejpam-6387	341	8	and	and	CCONJ
ejpam-6387	341	9	t.	t.	PROPN
ejpam-6387	341	10	hilberdink	hilberdink	NOUN
ejpam-6387	341	11	.	.	PUNCT
ejpam-6387	342	1	an	an	DET
ejpam-6387	342	2	example	example	NOUN
ejpam-6387	342	3	in	in	ADP
ejpam-6387	342	4	beurling	beurling	PROPN
ejpam-6387	342	5	’s	’s	PART
ejpam-6387	342	6	theory	theory	NOUN
ejpam-6387	342	7	of	of	ADP
ejpam-6387	342	8	generalised	generalise	VERB
ejpam-6387	342	9	primes	prime	NOUN
ejpam-6387	342	10	.	.	PUNCT
ejpam-6387	343	1	acta	acta	PROPN
ejpam-6387	343	2	arithmetica	arithmetica	PROPN
ejpam-6387	343	3	,	,	PUNCT
ejpam-6387	343	4	168:383–395	168:383–395	NUM
ejpam-6387	343	5	,	,	PUNCT
ejpam-6387	343	6	2015	2015	NUM
ejpam-6387	343	7	.	.	PUNCT
ejpam-6387	344	1	[	[	X
ejpam-6387	344	2	21	21	NUM
ejpam-6387	344	3	]	]	X
ejpam-6387	344	4	e.	e.	PROPN
ejpam-6387	344	5	c.	c.	PROPN
ejpam-6387	344	6	titchmarsh	titchmarsh	PROPN
ejpam-6387	344	7	.	.	PUNCT
ejpam-6387	345	1	the	the	DET
ejpam-6387	345	2	theory	theory	NOUN
ejpam-6387	345	3	of	of	ADP
ejpam-6387	345	4	functions	function	NOUN
ejpam-6387	345	5	.	.	PUNCT
ejpam-6387	346	1	wiley	wiley	PROPN
ejpam-6387	346	2	,	,	PUNCT
ejpam-6387	346	3	new	new	PROPN
ejpam-6387	346	4	york	york	PROPN
ejpam-6387	346	5	,	,	PUNCT
ejpam-6387	346	6	2	2	NUM
ejpam-6387	346	7	edition	edition	NOUN
ejpam-6387	346	8	,	,	PUNCT
ejpam-6387	346	9	1985	1985	NUM
ejpam-6387	346	10	.	.	PUNCT