id	sid	tid	token	lemma	pos
ejpam-2347	1	1	compile	compile	NOUN
ejpam-2347	1	2	/	/	SYM
ejpam-2347	1	3	output.dvi	output.dvi	NOUN
ejpam-2347	1	4	european	european	ADJ
ejpam-2347	1	5	journal	journal	NOUN
ejpam-2347	1	6	of	of	ADP
ejpam-2347	1	7	pure	pure	ADJ
ejpam-2347	1	8	and	and	CCONJ
ejpam-2347	1	9	applied	apply	VERB
ejpam-2347	1	10	mathematics	mathematic	NOUN
ejpam-2347	1	11	vol	vol	NOUN
ejpam-2347	1	12	.	.	PROPN
ejpam-2347	1	13	8	8	NUM
ejpam-2347	1	14	,	,	PUNCT
ejpam-2347	1	15	no	no	INTJ
ejpam-2347	1	16	.	.	NOUN
ejpam-2347	1	17	2	2	NUM
ejpam-2347	1	18	,	,	PUNCT
ejpam-2347	1	19	2015	2015	NUM
ejpam-2347	1	20	,	,	PUNCT
ejpam-2347	1	21	214	214	NUM
ejpam-2347	1	22	-	-	SYM
ejpam-2347	1	23	231	231	NUM
ejpam-2347	1	24	issn	issn	PROPN
ejpam-2347	1	25	1307	1307	NUM
ejpam-2347	1	26	-	-	SYM
ejpam-2347	1	27	5543	5543	NUM
ejpam-2347	1	28	–	–	PUNCT
ejpam-2347	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2347	1	30	some	some	DET
ejpam-2347	1	31	properties	property	NOUN
ejpam-2347	1	32	of	of	ADP
ejpam-2347	1	33	the	the	DET
ejpam-2347	1	34	p	p	NOUN
ejpam-2347	1	35	-	-	PUNCT
ejpam-2347	1	36	adic	adic	ADJ
ejpam-2347	1	37	beta	beta	NOUN
ejpam-2347	1	38	function	function	NOUN
ejpam-2347	1	39	hamza	hamza	PROPN
ejpam-2347	1	40	menken∗	menken∗	PROPN
ejpam-2347	1	41	,	,	PUNCT
ejpam-2347	1	42	özge	özge	PROPN
ejpam-2347	1	43	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	1	44	department	department	PROPN
ejpam-2347	1	45	of	of	ADP
ejpam-2347	1	46	mathematics	mathematics	PROPN
ejpam-2347	1	47	,	,	PUNCT
ejpam-2347	1	48	science	science	NOUN
ejpam-2347	1	49	and	and	CCONJ
ejpam-2347	1	50	arts	art	NOUN
ejpam-2347	1	51	faculty	faculty	PROPN
ejpam-2347	1	52	,	,	PUNCT
ejpam-2347	1	53	mersin	mersin	PROPN
ejpam-2347	1	54	university	university	PROPN
ejpam-2347	1	55	,	,	PUNCT
ejpam-2347	1	56	mersin	mersin	PROPN
ejpam-2347	1	57	,	,	PUNCT
ejpam-2347	1	58	turkey	turkey	NOUN
ejpam-2347	1	59	abstract	abstract	NOUN
ejpam-2347	1	60	.	.	PUNCT
ejpam-2347	2	1	in	in	ADP
ejpam-2347	2	2	the	the	DET
ejpam-2347	2	3	present	present	ADJ
ejpam-2347	2	4	work	work	NOUN
ejpam-2347	2	5	we	we	PRON
ejpam-2347	2	6	consider	consider	VERB
ejpam-2347	2	7	a	a	DET
ejpam-2347	2	8	p	p	ADJ
ejpam-2347	2	9	-	-	PUNCT
ejpam-2347	2	10	adic	adic	ADJ
ejpam-2347	2	11	analogue	analogue	NOUN
ejpam-2347	2	12	of	of	ADP
ejpam-2347	2	13	the	the	DET
ejpam-2347	2	14	classical	classical	ADJ
ejpam-2347	2	15	beta	beta	NOUN
ejpam-2347	2	16	function	function	NOUN
ejpam-2347	2	17	by	by	ADP
ejpam-2347	2	18	using	use	VERB
ejpam-2347	2	19	y.	y.	PROPN
ejpam-2347	2	20	morita	morita	PROPN
ejpam-2347	2	21	’s	’s	PART
ejpam-2347	2	22	p	p	ADJ
ejpam-2347	2	23	-	-	PUNCT
ejpam-2347	2	24	adic	adic	ADJ
ejpam-2347	2	25	gamma	gamma	NOUN
ejpam-2347	2	26	function	function	NOUN
ejpam-2347	2	27	.	.	PUNCT
ejpam-2347	3	1	we	we	PRON
ejpam-2347	3	2	obtain	obtain	VERB
ejpam-2347	3	3	some	some	DET
ejpam-2347	3	4	elementary	elementary	ADJ
ejpam-2347	3	5	properties	property	NOUN
ejpam-2347	3	6	of	of	ADP
ejpam-2347	3	7	the	the	DET
ejpam-2347	3	8	p	p	NOUN
ejpam-2347	3	9	-	-	PUNCT
ejpam-2347	3	10	adic	adic	ADJ
ejpam-2347	3	11	beta	beta	NOUN
ejpam-2347	3	12	function	function	NOUN
ejpam-2347	3	13	.	.	PUNCT
ejpam-2347	4	1	we	we	PRON
ejpam-2347	4	2	give	give	VERB
ejpam-2347	4	3	some	some	DET
ejpam-2347	4	4	relations	relation	NOUN
ejpam-2347	4	5	between	between	ADP
ejpam-2347	4	6	the	the	DET
ejpam-2347	4	7	classical	classical	ADJ
ejpam-2347	4	8	beta	beta	NOUN
ejpam-2347	4	9	and	and	CCONJ
ejpam-2347	4	10	the	the	DET
ejpam-2347	4	11	p	p	NOUN
ejpam-2347	4	12	-	-	PUNCT
ejpam-2347	4	13	adic	adic	ADJ
ejpam-2347	4	14	beta	beta	NOUN
ejpam-2347	4	15	functions	function	NOUN
ejpam-2347	4	16	at	at	ADP
ejpam-2347	4	17	the	the	DET
ejpam-2347	4	18	values	value	NOUN
ejpam-2347	4	19	of	of	ADP
ejpam-2347	4	20	natural	natural	ADJ
ejpam-2347	4	21	numbers	number	NOUN
ejpam-2347	4	22	.	.	PUNCT
ejpam-2347	5	1	2010	2010	NUM
ejpam-2347	5	2	mathematics	mathematic	NOUN
ejpam-2347	5	3	subject	subject	NOUN
ejpam-2347	5	4	classifications	classification	NOUN
ejpam-2347	5	5	:	:	PUNCT
ejpam-2347	5	6	11s80	11s80	NUM
ejpam-2347	5	7	;	;	PUNCT
ejpam-2347	5	8	11e95	11e95	NUM
ejpam-2347	5	9	key	key	ADJ
ejpam-2347	5	10	words	word	NOUN
ejpam-2347	5	11	and	and	CCONJ
ejpam-2347	5	12	phrases	phrase	NOUN
ejpam-2347	5	13	:	:	PUNCT
ejpam-2347	5	14	p	p	X
ejpam-2347	5	15	-	-	PUNCT
ejpam-2347	5	16	adic	adic	ADJ
ejpam-2347	5	17	number	number	NOUN
ejpam-2347	5	18	,	,	PUNCT
ejpam-2347	5	19	p	p	ADJ
ejpam-2347	5	20	-	-	PUNCT
ejpam-2347	5	21	adic	adic	ADJ
ejpam-2347	5	22	gamma	gamma	NOUN
ejpam-2347	5	23	function	function	NOUN
ejpam-2347	5	24	,	,	PUNCT
ejpam-2347	5	25	p	p	NOUN
ejpam-2347	5	26	-	-	PUNCT
ejpam-2347	5	27	adic	adic	ADJ
ejpam-2347	5	28	beta	beta	NOUN
ejpam-2347	5	29	function	function	NOUN
ejpam-2347	5	30	1	1	NUM
ejpam-2347	5	31	.	.	PUNCT
ejpam-2347	6	1	introduction	introduction	NOUN
ejpam-2347	6	2	let	let	VERB
ejpam-2347	6	3	p	p	NOUN
ejpam-2347	6	4	be	be	AUX
ejpam-2347	6	5	fixed	fix	VERB
ejpam-2347	6	6	prime	prime	ADJ
ejpam-2347	6	7	number	number	NOUN
ejpam-2347	6	8	.	.	PUNCT
ejpam-2347	7	1	it	it	PRON
ejpam-2347	7	2	is	be	AUX
ejpam-2347	7	3	well	well	ADV
ejpam-2347	7	4	known	know	VERB
ejpam-2347	7	5	that	that	SCONJ
ejpam-2347	7	6	the	the	DET
ejpam-2347	7	7	p−adic	p−adic	ADJ
ejpam-2347	7	8	valuation	valuation	NOUN
ejpam-2347	7	9	of	of	ADP
ejpam-2347	7	10	any	any	DET
ejpam-2347	7	11	x	x	SYM
ejpam-2347	7	12	∈	∈	PROPN
ejpam-2347	7	13	q	q	NOUN
ejpam-2347	7	14	,	,	PUNCT
ejpam-2347	7	15	x	x	SYM
ejpam-2347	7	16	6=	6=	NUM
ejpam-2347	7	17	0	0	NUM
ejpam-2347	7	18	is	be	AUX
ejpam-2347	7	19	determined	determine	VERB
ejpam-2347	7	20	by	by	ADP
ejpam-2347	7	21	the	the	DET
ejpam-2347	7	22	formula	formula	NOUN
ejpam-2347	7	23	x	x	PUNCT
ejpam-2347	7	24	=	=	SYM
ejpam-2347	7	25	pvp(x	pvp(x	PROPN
ejpam-2347	7	26	)	)	PUNCT
ejpam-2347	7	27	.	.	PUNCT
ejpam-2347	8	1	a	a	DET
ejpam-2347	8	2	b	b	NOUN
ejpam-2347	8	3	where	where	SCONJ
ejpam-2347	8	4	vp(x	vp(x	NOUN
ejpam-2347	8	5	)	)	PUNCT
ejpam-2347	8	6	∈	∈	PROPN
ejpam-2347	8	7	z	z	PROPN
ejpam-2347	8	8	and	and	CCONJ
ejpam-2347	8	9	ab	ab	PROPN
ejpam-2347	8	10	is	be	AUX
ejpam-2347	8	11	not	not	PART
ejpam-2347	8	12	divided	divide	VERB
ejpam-2347	8	13	by	by	ADP
ejpam-2347	8	14	p.	p.	VERB
ejpam-2347	8	15	the	the	DET
ejpam-2347	8	16	p	p	ADJ
ejpam-2347	8	17	-	-	PUNCT
ejpam-2347	8	18	adic	adic	ADJ
ejpam-2347	8	19	norm	norm	NOUN
ejpam-2347	8	20	|·|p	|·|p	NOUN
ejpam-2347	8	21	is	be	AUX
ejpam-2347	8	22	defined	define	VERB
ejpam-2347	8	23	by	by	ADP
ejpam-2347	8	24	|x	|x	NOUN
ejpam-2347	8	25	|p	|p	NOUN
ejpam-2347	8	26	=	=	SYM
ejpam-2347	8	27	¨	¨	NOUN
ejpam-2347	8	28	p−vp(x	p−vp(x	PROPN
ejpam-2347	8	29	)	)	PUNCT
ejpam-2347	8	30	,	,	PUNCT
ejpam-2347	8	31	x	x	X
ejpam-2347	8	32	6=	6=	ADP
ejpam-2347	8	33	0	0	NUM
ejpam-2347	8	34	0	0	NUM
ejpam-2347	8	35	,	,	PUNCT
ejpam-2347	8	36	x	x	SYM
ejpam-2347	9	1	=	=	PUNCT
ejpam-2347	9	2	0	0	NUM
ejpam-2347	9	3	.	.	PUNCT
ejpam-2347	10	1	by	by	ADP
ejpam-2347	10	2	qp	qp	NOUN
ejpam-2347	10	3	we	we	PRON
ejpam-2347	10	4	denote	denote	VERB
ejpam-2347	10	5	the	the	DET
ejpam-2347	10	6	completion	completion	NOUN
ejpam-2347	10	7	of	of	ADP
ejpam-2347	10	8	rational	rational	ADJ
ejpam-2347	10	9	numbers	number	NOUN
ejpam-2347	10	10	field	field	VERB
ejpam-2347	10	11	q	q	PUNCT
ejpam-2347	10	12	with	with	ADP
ejpam-2347	10	13	respect	respect	NOUN
ejpam-2347	10	14	to	to	ADP
ejpam-2347	10	15	the	the	DET
ejpam-2347	10	16	p	p	NOUN
ejpam-2347	10	17	-	-	PUNCT
ejpam-2347	10	18	adic	adic	ADJ
ejpam-2347	10	19	norm	norm	NOUN
ejpam-2347	10	20	|·|p	|·|p	NOUN
ejpam-2347	10	21	.	.	PUNCT
ejpam-2347	11	1	the	the	DET
ejpam-2347	11	2	ring	ring	NOUN
ejpam-2347	11	3	of	of	ADP
ejpam-2347	11	4	p	p	NOUN
ejpam-2347	11	5	-	-	PUNCT
ejpam-2347	11	6	adic	adic	ADJ
ejpam-2347	11	7	integers	integer	NOUN
ejpam-2347	11	8	is	be	AUX
ejpam-2347	11	9	the	the	DET
ejpam-2347	11	10	valuation	valuation	NOUN
ejpam-2347	11	11	ring	ring	NOUN
ejpam-2347	11	12	zp	zp	PROPN
ejpam-2347	11	13	=	=	SYM
ejpam-2347	11	14	�	�	PROPN
ejpam-2347	11	15	x	x	SYM
ejpam-2347	11	16	∈	∈	NOUN
ejpam-2347	11	17	qp	qp	NOUN
ejpam-2347	11	18	:	:	PUNCT
ejpam-2347	11	19	|x	|x	NOUN
ejpam-2347	11	20	|p	|p	VERB
ejpam-2347	11	21	≤	≤	ADV
ejpam-2347	11	22	1	1	NUM
ejpam-2347	11	23	.	.	PUNCT
ejpam-2347	12	1	note	note	VERB
ejpam-2347	12	2	that	that	SCONJ
ejpam-2347	12	3	every	every	DET
ejpam-2347	12	4	x	x	X
ejpam-2347	12	5	∈	∈	PROPN
ejpam-2347	12	6	zp	zp	NOUN
ejpam-2347	12	7	can	can	AUX
ejpam-2347	12	8	be	be	AUX
ejpam-2347	12	9	written	write	VERB
ejpam-2347	12	10	in	in	ADP
ejpam-2347	12	11	the	the	DET
ejpam-2347	12	12	form	form	NOUN
ejpam-2347	12	13	x	x	NOUN
ejpam-2347	12	14	=	=	SYM
ejpam-2347	12	15	b0	b0	NOUN
ejpam-2347	12	16	+	+	CCONJ
ejpam-2347	12	17	b1p+	b1p+	NOUN
ejpam-2347	12	18	b2p2	b2p2	NOUN
ejpam-2347	12	19	+	+	PUNCT
ejpam-2347	12	20	.	.	PUNCT
ejpam-2347	12	21	.	.	PUNCT
ejpam-2347	13	1	.+	.+	NOUN
ejpam-2347	13	2	bnpn	bnpn	ADV
ejpam-2347	13	3	+	+	PUNCT
ejpam-2347	13	4	.	.	PUNCT
ejpam-2347	13	5	.	.	PUNCT
ejpam-2347	13	6	.	.	PUNCT
ejpam-2347	14	1	∗corresponding	∗corresponde	VERB
ejpam-2347	14	2	author	author	NOUN
ejpam-2347	14	3	.	.	PUNCT
ejpam-2347	15	1	email	email	NOUN
ejpam-2347	15	2	addresses	address	NOUN
ejpam-2347	15	3	:	:	PUNCT
ejpam-2347	15	4	hmenken@mersin.edu.tr	hmenken@mersin.edu.tr	PROPN
ejpam-2347	15	5	(	(	PUNCT
ejpam-2347	15	6	h.	h.	PROPN
ejpam-2347	15	7	menken	menken	PROPN
ejpam-2347	15	8	)	)	PUNCT
ejpam-2347	15	9	,	,	PUNCT
ejpam-2347	15	10	ozgecolakoglu@mersin.edu.tr	ozgecolakoglu@mersin.edu.tr	PROPN
ejpam-2347	15	11	(	(	PUNCT
ejpam-2347	15	12	ö.	ö.	PROPN
ejpam-2347	15	13	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	15	14	)	)	PUNCT
ejpam-2347	15	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2347	16	1	214	214	NUM
ejpam-2347	16	2	c	c	X
ejpam-2347	16	3	©	©	PROPN
ejpam-2347	16	4	2015	2015	NUM
ejpam-2347	16	5	ejpam	ejpam	NOUN
ejpam-2347	16	6	all	all	DET
ejpam-2347	16	7	rights	right	NOUN
ejpam-2347	16	8	reserved	reserve	VERB
ejpam-2347	16	9	.	.	PUNCT
ejpam-2347	17	1	h.	h.	PROPN
ejpam-2347	17	2	menken	menken	PROPN
ejpam-2347	17	3	,	,	PUNCT
ejpam-2347	17	4	ö.	ö.	VERB
ejpam-2347	17	5	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	17	6	/	/	SYM
ejpam-2347	17	7	eur	eur	PROPN
ejpam-2347	17	8	.	.	PUNCT
ejpam-2347	18	1	j.	j.	PROPN
ejpam-2347	18	2	pure	pure	PROPN
ejpam-2347	18	3	appl	appl	PROPN
ejpam-2347	18	4	.	.	PROPN
ejpam-2347	18	5	math	math	PROPN
ejpam-2347	18	6	,	,	PUNCT
ejpam-2347	18	7	8	8	NUM
ejpam-2347	18	8	(	(	PUNCT
ejpam-2347	18	9	2015	2015	NUM
ejpam-2347	18	10	)	)	PUNCT
ejpam-2347	18	11	,	,	PUNCT
ejpam-2347	18	12	214	214	NUM
ejpam-2347	18	13	-	-	SYM
ejpam-2347	18	14	231	231	NUM
ejpam-2347	18	15	215	215	NUM
ejpam-2347	18	16	with	with	ADP
ejpam-2347	18	17	0≤	0≤	ADJ
ejpam-2347	18	18	bi	bi	NOUN
ejpam-2347	18	19	≤	≤	NOUN
ejpam-2347	18	20	p−	p−	NOUN
ejpam-2347	18	21	1	1	NUM
ejpam-2347	18	22	;	;	PUNCT
ejpam-2347	18	23	and	and	CCONJ
ejpam-2347	18	24	also	also	ADV
ejpam-2347	18	25	,	,	PUNCT
ejpam-2347	18	26	every	every	DET
ejpam-2347	18	27	x	x	PROPN
ejpam-2347	18	28	∈	∈	NOUN
ejpam-2347	18	29	qp	qp	NOUN
ejpam-2347	18	30	can	can	AUX
ejpam-2347	18	31	be	be	AUX
ejpam-2347	18	32	written	write	VERB
ejpam-2347	18	33	in	in	ADP
ejpam-2347	18	34	the	the	DET
ejpam-2347	18	35	form	form	NOUN
ejpam-2347	18	36	x	x	PUNCT
ejpam-2347	19	1	=	=	SYM
ejpam-2347	19	2	b−n0	b−n0	PART
ejpam-2347	19	3	p−n0	p−n0	NOUN
ejpam-2347	19	4	+	+	X
ejpam-2347	19	5	.	.	PUNCT
ejpam-2347	19	6	.	.	PUNCT
ejpam-2347	20	1	.+	.+	NOUN
ejpam-2347	20	2	b0	b0	NOUN
ejpam-2347	20	3	+	+	CCONJ
ejpam-2347	20	4	b1p+	b1p+	NOUN
ejpam-2347	20	5	b2p2	b2p2	NOUN
ejpam-2347	20	6	+	+	PUNCT
ejpam-2347	20	7	.	.	PUNCT
ejpam-2347	20	8	.	.	PUNCT
ejpam-2347	21	1	.+	.+	NOUN
ejpam-2347	21	2	bnpn	bnpn	ADV
ejpam-2347	21	3	+	+	PUNCT
ejpam-2347	21	4	.	.	PUNCT
ejpam-2347	21	5	.	.	PUNCT
ejpam-2347	22	1	.=	.=	VERB
ejpam-2347	22	2	∑	∑	PUNCT
ejpam-2347	22	3	n≥−n0	n≥−n0	ADJ
ejpam-2347	22	4	bnpn	bnpn	ADV
ejpam-2347	22	5	with	with	ADP
ejpam-2347	22	6	0≤	0≤	ADJ
ejpam-2347	22	7	bi	bi	NOUN
ejpam-2347	22	8	≤	≤	NOUN
ejpam-2347	22	9	p−	p−	NOUN
ejpam-2347	22	10	1	1	NUM
ejpam-2347	22	11	and	and	CCONJ
ejpam-2347	22	12	−n0	−n0	PROPN
ejpam-2347	22	13	=	=	SYM
ejpam-2347	22	14	vp(x	vp(x	PROPN
ejpam-2347	22	15	)	)	PUNCT
ejpam-2347	22	16	(	(	PUNCT
ejpam-2347	22	17	for	for	SCONJ
ejpam-2347	22	18	details	detail	NOUN
ejpam-2347	22	19	see	see	VERB
ejpam-2347	22	20	[	[	X
ejpam-2347	22	21	12	12	NUM
ejpam-2347	22	22	]	]	NUM
ejpam-2347	22	23	)	)	PUNCT
ejpam-2347	22	24	.	.	PUNCT
ejpam-2347	23	1	the	the	DET
ejpam-2347	23	2	classical	classical	ADJ
ejpam-2347	23	3	gamma	gamma	NOUN
ejpam-2347	23	4	function	function	NOUN
ejpam-2347	23	5	is	be	AUX
ejpam-2347	23	6	an	an	DET
ejpam-2347	23	7	extension	extension	NOUN
ejpam-2347	23	8	of	of	ADP
ejpam-2347	23	9	the	the	DET
ejpam-2347	23	10	factorial	factorial	ADJ
ejpam-2347	23	11	function	function	NOUN
ejpam-2347	23	12	and	and	CCONJ
ejpam-2347	23	13	is	be	AUX
ejpam-2347	23	14	defined	define	VERB
ejpam-2347	23	15	by	by	ADP
ejpam-2347	23	16	the	the	DET
ejpam-2347	23	17	formula	formula	NOUN
ejpam-2347	23	18	γ(x	γ(x	NOUN
ejpam-2347	23	19	)	)	PUNCT
ejpam-2347	23	20	=	=	SYM
ejpam-2347	24	1	∞	∞	NUM
ejpam-2347	24	2	∫	∫	NOUN
ejpam-2347	24	3	0	0	NUM
ejpam-2347	25	1	t	t	NOUN
ejpam-2347	25	2	x−1e−t	x−1e−t	PROPN
ejpam-2347	26	1	d	d	PROPN
ejpam-2347	26	2	t	t	PROPN
ejpam-2347	26	3	for	for	ADP
ejpam-2347	26	4	all	all	PRON
ejpam-2347	26	5	re	re	ADP
ejpam-2347	26	6	(	(	PUNCT
ejpam-2347	26	7	x	x	X
ejpam-2347	26	8	)	)	PUNCT
ejpam-2347	26	9	>	>	X
ejpam-2347	26	10	0	0	PUNCT
ejpam-2347	27	1	[	[	X
ejpam-2347	27	2	1	1	NUM
ejpam-2347	27	3	]	]	PUNCT
ejpam-2347	27	4	.	.	PUNCT
ejpam-2347	28	1	the	the	DET
ejpam-2347	28	2	basic	basic	ADJ
ejpam-2347	28	3	properties	property	NOUN
ejpam-2347	28	4	of	of	ADP
ejpam-2347	28	5	the	the	DET
ejpam-2347	28	6	classical	classical	ADJ
ejpam-2347	28	7	gamma	gamma	NOUN
ejpam-2347	28	8	function	function	NOUN
ejpam-2347	28	9	are	be	AUX
ejpam-2347	28	10	following	follow	VERB
ejpam-2347	28	11	:	:	PUNCT
ejpam-2347	28	12	(	(	PUNCT
ejpam-2347	28	13	i	i	NOUN
ejpam-2347	28	14	)	)	PUNCT
ejpam-2347	28	15	γ(n+	γ(n+	PRON
ejpam-2347	28	16	1	1	NUM
ejpam-2347	28	17	)	)	PUNCT
ejpam-2347	28	18	=	=	SYM
ejpam-2347	28	19	n	n	X
ejpam-2347	28	20	!	!	X
ejpam-2347	29	1	for	for	ADP
ejpam-2347	29	2	all	all	DET
ejpam-2347	29	3	non	non	PRON
ejpam-2347	29	4	negative	negative	ADJ
ejpam-2347	29	5	integer	integer	NOUN
ejpam-2347	29	6	n	n	PROPN
ejpam-2347	29	7	(	(	PUNCT
ejpam-2347	29	8	ii	ii	NOUN
ejpam-2347	29	9	)	)	PUNCT
ejpam-2347	29	10	γ(z	γ(z	PROPN
ejpam-2347	29	11	+	+	CCONJ
ejpam-2347	29	12	1	1	NUM
ejpam-2347	29	13	)	)	PUNCT
ejpam-2347	29	14	=	=	SYM
ejpam-2347	29	15	zγ(z	zγ(z	NUM
ejpam-2347	29	16	)	)	PUNCT
ejpam-2347	29	17	(	(	PUNCT
ejpam-2347	29	18	re	re	X
ejpam-2347	29	19	(	(	PUNCT
ejpam-2347	29	20	z	z	NOUN
ejpam-2347	29	21	)	)	PUNCT
ejpam-2347	29	22	>	>	X
ejpam-2347	29	23	0	0	NUM
ejpam-2347	29	24	)	)	PUNCT
ejpam-2347	29	25	(	(	PUNCT
ejpam-2347	29	26	iii	iii	X
ejpam-2347	29	27	)	)	PUNCT
ejpam-2347	29	28	γ(1−	γ(1−	NOUN
ejpam-2347	29	29	z)γ(z	z)γ(z	NUM
ejpam-2347	29	30	)	)	PUNCT
ejpam-2347	29	31	=	=	PUNCT
ejpam-2347	29	32	π	π	NOUN
ejpam-2347	29	33	sin(πz	sin(πz	NOUN
ejpam-2347	29	34	)	)	PUNCT
ejpam-2347	29	35	(	(	PUNCT
ejpam-2347	29	36	re	re	X
ejpam-2347	29	37	(	(	PUNCT
ejpam-2347	29	38	z	z	NOUN
ejpam-2347	29	39	)	)	PUNCT
ejpam-2347	29	40	>	>	X
ejpam-2347	29	41	0	0	NUM
ejpam-2347	29	42	)	)	PUNCT
ejpam-2347	29	43	(	(	PUNCT
ejpam-2347	29	44	iv	iv	X
ejpam-2347	29	45	)	)	PUNCT
ejpam-2347	29	46	γ(1	γ(1	PROPN
ejpam-2347	29	47	2	2	NUM
ejpam-2347	29	48	)	)	PUNCT
ejpam-2347	29	49	=	=	PUNCT
ejpam-2347	29	50	p	p	X
ejpam-2347	29	51	π	π	PROPN
ejpam-2347	29	52	.	.	PUNCT
ejpam-2347	30	1	it	it	PRON
ejpam-2347	30	2	is	be	AUX
ejpam-2347	30	3	well	well	ADV
ejpam-2347	30	4	known	know	VERB
ejpam-2347	30	5	that	that	SCONJ
ejpam-2347	30	6	the	the	DET
ejpam-2347	30	7	classical	classical	ADJ
ejpam-2347	30	8	beta	beta	NOUN
ejpam-2347	30	9	function	function	NOUN
ejpam-2347	30	10	b(x	b(x	NOUN
ejpam-2347	30	11	,	,	PUNCT
ejpam-2347	30	12	y	y	PROPN
ejpam-2347	30	13	)	)	PUNCT
ejpam-2347	30	14	is	be	AUX
ejpam-2347	30	15	defined	define	VERB
ejpam-2347	30	16	by	by	ADP
ejpam-2347	30	17	b(x	b(x	PROPN
ejpam-2347	30	18	,	,	PUNCT
ejpam-2347	30	19	y	y	NOUN
ejpam-2347	30	20	)	)	PUNCT
ejpam-2347	30	21	=	=	SYM
ejpam-2347	30	22	γ(x)γ(y	γ(x)γ(y	PROPN
ejpam-2347	30	23	)	)	PUNCT
ejpam-2347	30	24	γ(x	γ(x	PROPN
ejpam-2347	31	1	+	+	CCONJ
ejpam-2347	31	2	y	y	NOUN
ejpam-2347	31	3	)	)	PUNCT
ejpam-2347	31	4	and	and	CCONJ
ejpam-2347	31	5	it	it	PRON
ejpam-2347	31	6	has	have	VERB
ejpam-2347	31	7	the	the	DET
ejpam-2347	31	8	integral	integral	ADJ
ejpam-2347	31	9	representation	representation	NOUN
ejpam-2347	31	10	b(x	b(x	NOUN
ejpam-2347	31	11	,	,	PUNCT
ejpam-2347	31	12	y	y	NOUN
ejpam-2347	31	13	)	)	PUNCT
ejpam-2347	32	1	=	=	SYM
ejpam-2347	32	2	1	1	NUM
ejpam-2347	32	3	∫	∫	NOUN
ejpam-2347	32	4	0	0	NUM
ejpam-2347	32	5	t	t	PROPN
ejpam-2347	32	6	x−1	x−1	PROPN
ejpam-2347	33	1	(	(	PUNCT
ejpam-2347	33	2	1−	1−	NUM
ejpam-2347	33	3	t)y−1	t)y−1	PROPN
ejpam-2347	33	4	d	d	PROPN
ejpam-2347	33	5	t	t	PROPN
ejpam-2347	33	6	for	for	ADP
ejpam-2347	33	7	all	all	PRON
ejpam-2347	33	8	re	re	ADP
ejpam-2347	33	9	(	(	PUNCT
ejpam-2347	33	10	x	x	X
ejpam-2347	33	11	)	)	PUNCT
ejpam-2347	33	12	,	,	PUNCT
ejpam-2347	33	13	re	re	VERB
ejpam-2347	33	14	�	�	PROPN
ejpam-2347	33	15	y	y	PROPN
ejpam-2347	33	16	�	�	PROPN
ejpam-2347	33	17	>	>	X
ejpam-2347	33	18	0	0	PROPN
ejpam-2347	33	19	.	.	PUNCT
ejpam-2347	34	1	the	the	DET
ejpam-2347	34	2	basic	basic	ADJ
ejpam-2347	34	3	properties	property	NOUN
ejpam-2347	34	4	of	of	ADP
ejpam-2347	34	5	the	the	DET
ejpam-2347	34	6	classical	classical	ADJ
ejpam-2347	34	7	beta	beta	NOUN
ejpam-2347	34	8	function	function	NOUN
ejpam-2347	34	9	are	be	AUX
ejpam-2347	34	10	the	the	DET
ejpam-2347	34	11	following	follow	VERB
ejpam-2347	34	12	:	:	PUNCT
ejpam-2347	34	13	(	(	PUNCT
ejpam-2347	34	14	i	i	NOUN
ejpam-2347	34	15	)	)	PUNCT
ejpam-2347	34	16	b(x	b(x	NOUN
ejpam-2347	34	17	,	,	PUNCT
ejpam-2347	34	18	y	y	NOUN
ejpam-2347	34	19	)	)	PUNCT
ejpam-2347	35	1	=	=	SYM
ejpam-2347	35	2	b(y	b(y	PROPN
ejpam-2347	35	3	,	,	PUNCT
ejpam-2347	35	4	x	x	X
ejpam-2347	35	5	)	)	PUNCT
ejpam-2347	35	6	(	(	PUNCT
ejpam-2347	35	7	ii	ii	NOUN
ejpam-2347	35	8	)	)	PUNCT
ejpam-2347	35	9	b(x	b(x	NOUN
ejpam-2347	35	10	+	+	CCONJ
ejpam-2347	35	11	1	1	NUM
ejpam-2347	35	12	,	,	PUNCT
ejpam-2347	35	13	y	y	NOUN
ejpam-2347	35	14	)	)	PUNCT
ejpam-2347	35	15	=	=	VERB
ejpam-2347	36	1	b(x	b(x	NOUN
ejpam-2347	36	2	,	,	PUNCT
ejpam-2347	36	3	y	y	PROPN
ejpam-2347	36	4	)	)	PUNCT
ejpam-2347	36	5	x	x	X
ejpam-2347	36	6	x+y	x+y	NUM
ejpam-2347	36	7	(	(	PUNCT
ejpam-2347	36	8	iii	iii	NOUN
ejpam-2347	36	9	)	)	PUNCT
ejpam-2347	36	10	b(x	b(x	NOUN
ejpam-2347	36	11	,	,	PUNCT
ejpam-2347	36	12	y	y	PROPN
ejpam-2347	36	13	+	+	NOUN
ejpam-2347	36	14	1	1	X
ejpam-2347	36	15	)	)	PUNCT
ejpam-2347	36	16	=	=	VERB
ejpam-2347	37	1	b(x	b(x	NOUN
ejpam-2347	37	2	,	,	PUNCT
ejpam-2347	37	3	y	y	PROPN
ejpam-2347	37	4	)	)	PUNCT
ejpam-2347	37	5	y	y	PROPN
ejpam-2347	37	6	x+y	x+y	NUM
ejpam-2347	37	7	(	(	PUNCT
ejpam-2347	37	8	iv	iv	X
ejpam-2347	37	9	)	)	PUNCT
ejpam-2347	37	10	b(x	b(x	NOUN
ejpam-2347	37	11	,	,	PUNCT
ejpam-2347	37	12	y)b(x	y)b(x	PROPN
ejpam-2347	37	13	+	+	PROPN
ejpam-2347	37	14	y	y	PROPN
ejpam-2347	37	15	,	,	PUNCT
ejpam-2347	37	16	1−	1−	NUM
ejpam-2347	37	17	y	y	NOUN
ejpam-2347	37	18	)	)	PUNCT
ejpam-2347	38	1	=	=	SYM
ejpam-2347	38	2	π	π	NOUN
ejpam-2347	38	3	x	x	PUNCT
ejpam-2347	38	4	sin(πy	sin(πy	NOUN
ejpam-2347	38	5	)	)	PUNCT
ejpam-2347	38	6	(	(	PUNCT
ejpam-2347	38	7	v	v	NOUN
ejpam-2347	38	8	)	)	PUNCT
ejpam-2347	38	9	�	�	PROPN
ejpam-2347	38	10	n	n	CCONJ
ejpam-2347	38	11	k	k	PROPN
ejpam-2347	38	12	�	�	PROPN
ejpam-2347	38	13	=	=	SYM
ejpam-2347	38	14	1	1	NUM
ejpam-2347	38	15	(	(	PUNCT
ejpam-2347	38	16	n+1)b(n−k+1,k+1	n+1)b(n−k+1,k+1	NUM
ejpam-2347	38	17	)	)	PUNCT
ejpam-2347	38	18	(	(	PUNCT
ejpam-2347	38	19	n	n	X
ejpam-2347	38	20	,	,	PUNCT
ejpam-2347	38	21	k	k	PROPN
ejpam-2347	38	22	∈	∈	PROPN
ejpam-2347	38	23	n	n	CCONJ
ejpam-2347	38	24	,	,	PUNCT
ejpam-2347	38	25	k	k	PROPN
ejpam-2347	38	26	≤	≤	PROPN
ejpam-2347	38	27	n	n	CCONJ
ejpam-2347	38	28	)	)	PUNCT
ejpam-2347	38	29	(	(	PUNCT
ejpam-2347	38	30	vi	vi	NOUN
ejpam-2347	38	31	)	)	PUNCT
ejpam-2347	38	32	b(1	b(1	PROPN
ejpam-2347	38	33	2	2	NUM
ejpam-2347	38	34	,	,	PUNCT
ejpam-2347	38	35	1	1	NUM
ejpam-2347	38	36	2	2	NUM
ejpam-2347	38	37	)	)	PUNCT
ejpam-2347	38	38	=	=	PUNCT
ejpam-2347	39	1	π	π	PROPN
ejpam-2347	39	2	h.	h.	PROPN
ejpam-2347	39	3	menken	menken	PROPN
ejpam-2347	39	4	,	,	PUNCT
ejpam-2347	39	5	ö.	ö.	VERB
ejpam-2347	39	6	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	39	7	/	/	SYM
ejpam-2347	39	8	eur	eur	PROPN
ejpam-2347	39	9	.	.	PUNCT
ejpam-2347	40	1	j.	j.	PROPN
ejpam-2347	40	2	pure	pure	PROPN
ejpam-2347	40	3	appl	appl	PROPN
ejpam-2347	40	4	.	.	PROPN
ejpam-2347	40	5	math	math	PROPN
ejpam-2347	40	6	,	,	PUNCT
ejpam-2347	40	7	8	8	NUM
ejpam-2347	40	8	(	(	PUNCT
ejpam-2347	40	9	2015	2015	NUM
ejpam-2347	40	10	)	)	PUNCT
ejpam-2347	40	11	,	,	PUNCT
ejpam-2347	40	12	214	214	NUM
ejpam-2347	40	13	-	-	SYM
ejpam-2347	40	14	231	231	NUM
ejpam-2347	40	15	216	216	NUM
ejpam-2347	40	16	(	(	PUNCT
ejpam-2347	40	17	vii	vii	PROPN
ejpam-2347	40	18	)	)	PUNCT
ejpam-2347	40	19	b(x	b(x	NOUN
ejpam-2347	40	20	+	+	CCONJ
ejpam-2347	40	21	1	1	NUM
ejpam-2347	40	22	,	,	PUNCT
ejpam-2347	40	23	y	y	NOUN
ejpam-2347	40	24	)	)	PUNCT
ejpam-2347	41	1	+	+	CCONJ
ejpam-2347	42	1	b(x	b(x	NOUN
ejpam-2347	42	2	,	,	PUNCT
ejpam-2347	42	3	y	y	PROPN
ejpam-2347	42	4	+	+	NOUN
ejpam-2347	42	5	1	1	X
ejpam-2347	42	6	)	)	PUNCT
ejpam-2347	42	7	=	=	VERB
ejpam-2347	43	1	b(x	b(x	NOUN
ejpam-2347	43	2	,	,	PUNCT
ejpam-2347	43	3	y	y	PROPN
ejpam-2347	43	4	)	)	PUNCT
ejpam-2347	43	5	(	(	PUNCT
ejpam-2347	43	6	viii	viii	NOUN
ejpam-2347	43	7	)	)	PUNCT
ejpam-2347	43	8	b(x	b(x	NOUN
ejpam-2347	43	9	,	,	PUNCT
ejpam-2347	43	10	y	y	PROPN
ejpam-2347	43	11	+	+	NOUN
ejpam-2347	43	12	1	1	X
ejpam-2347	43	13	)	)	PUNCT
ejpam-2347	43	14	=	=	SYM
ejpam-2347	43	15	y	y	NOUN
ejpam-2347	43	16	x	x	PUNCT
ejpam-2347	43	17	b(x	b(x	NOUN
ejpam-2347	43	18	+	+	CCONJ
ejpam-2347	43	19	1	1	NUM
ejpam-2347	43	20	,	,	PUNCT
ejpam-2347	43	21	y	y	NOUN
ejpam-2347	43	22	)	)	PUNCT
ejpam-2347	43	23	=	=	SYM
ejpam-2347	44	1	y	y	PROPN
ejpam-2347	44	2	x+y	x+y	PROPN
ejpam-2347	44	3	b(x	b(x	NOUN
ejpam-2347	44	4	,	,	PUNCT
ejpam-2347	44	5	y	y	PROPN
ejpam-2347	44	6	)	)	PUNCT
ejpam-2347	44	7	(	(	PUNCT
ejpam-2347	44	8	ix	ix	ADV
ejpam-2347	44	9	)	)	PUNCT
ejpam-2347	44	10	b(x	b(x	NOUN
ejpam-2347	44	11	,	,	PUNCT
ejpam-2347	44	12	y)b(x	y)b(x	PROPN
ejpam-2347	44	13	+	+	PROPN
ejpam-2347	44	14	y	y	PROPN
ejpam-2347	44	15	,	,	PUNCT
ejpam-2347	44	16	z)b(x	z)b(x	VERB
ejpam-2347	44	17	+	+	CCONJ
ejpam-2347	44	18	y	y	PROPN
ejpam-2347	44	19	+	+	PROPN
ejpam-2347	44	20	z	z	PROPN
ejpam-2347	44	21	,	,	PUNCT
ejpam-2347	44	22	w	w	NOUN
ejpam-2347	44	23	)	)	PUNCT
ejpam-2347	44	24	=	=	SYM
ejpam-2347	44	25	γ(x)γ(y)γ(z)γ(w	γ(x)γ(y)γ(z)γ(w	PROPN
ejpam-2347	44	26	)	)	PUNCT
ejpam-2347	44	27	γ(x+y+z+w	γ(x+y+z+w	PROPN
ejpam-2347	44	28	)	)	PUNCT
ejpam-2347	44	29	where	where	SCONJ
ejpam-2347	44	30	re	re	X
ejpam-2347	44	31	(	(	PUNCT
ejpam-2347	44	32	x	x	X
ejpam-2347	44	33	)	)	PUNCT
ejpam-2347	44	34	,	,	PUNCT
ejpam-2347	44	35	re	re	VERB
ejpam-2347	44	36	�	�	PROPN
ejpam-2347	44	37	y	y	PROPN
ejpam-2347	44	38	�	�	PROPN
ejpam-2347	44	39	,	,	PUNCT
ejpam-2347	44	40	re	re	X
ejpam-2347	44	41	(	(	PUNCT
ejpam-2347	44	42	z	z	NOUN
ejpam-2347	44	43	)	)	PUNCT
ejpam-2347	44	44	,	,	PUNCT
ejpam-2347	44	45	re	re	X
ejpam-2347	44	46	(	(	PUNCT
ejpam-2347	44	47	w	w	NOUN
ejpam-2347	44	48	)	)	PUNCT
ejpam-2347	44	49	>	>	X
ejpam-2347	45	1	0	0	X
ejpam-2347	45	2	.	.	PUNCT
ejpam-2347	46	1	the	the	DET
ejpam-2347	46	2	p	p	ADJ
ejpam-2347	46	3	-	-	PUNCT
ejpam-2347	46	4	adic	adic	ADJ
ejpam-2347	46	5	analogue	analogue	NOUN
ejpam-2347	46	6	of	of	ADP
ejpam-2347	46	7	the	the	DET
ejpam-2347	46	8	classical	classical	ADJ
ejpam-2347	46	9	gamma	gamma	NOUN
ejpam-2347	46	10	function	function	NOUN
ejpam-2347	46	11	depends	depend	VERB
ejpam-2347	46	12	on	on	ADP
ejpam-2347	46	13	the	the	DET
ejpam-2347	46	14	p	p	NOUN
ejpam-2347	46	15	-	-	PUNCT
ejpam-2347	46	16	adic	adic	ADJ
ejpam-2347	46	17	version	version	NOUN
ejpam-2347	46	18	of	of	ADP
ejpam-2347	46	19	factorial	factorial	ADJ
ejpam-2347	46	20	function	function	NOUN
ejpam-2347	46	21	.	.	PUNCT
ejpam-2347	47	1	the	the	DET
ejpam-2347	47	2	p	p	NOUN
ejpam-2347	47	3	-	-	PUNCT
ejpam-2347	47	4	adic	adic	ADJ
ejpam-2347	47	5	version	version	NOUN
ejpam-2347	47	6	of	of	ADP
ejpam-2347	47	7	factorial	factorial	ADJ
ejpam-2347	47	8	function	function	NOUN
ejpam-2347	47	9	is	be	AUX
ejpam-2347	47	10	defined	define	VERB
ejpam-2347	47	11	by	by	ADP
ejpam-2347	47	12	(	(	PUNCT
ejpam-2347	47	13	n!)p	n!)p	NUM
ejpam-2347	47	14	:	:	PUNCT
ejpam-2347	48	1	=	=	SYM
ejpam-2347	48	2	∏	∏	PROPN
ejpam-2347	48	3	1≤	1≤	NUM
ejpam-2347	48	4	j	j	PROPN
ejpam-2347	48	5	≤	≤	PROPN
ejpam-2347	48	6	n	n	CCONJ
ejpam-2347	48	7	(	(	PUNCT
ejpam-2347	48	8	j	j	PROPN
ejpam-2347	48	9	,	,	PUNCT
ejpam-2347	48	10	p	p	NOUN
ejpam-2347	48	11	)	)	PUNCT
ejpam-2347	48	12	=	=	SYM
ejpam-2347	48	13	1	1	NUM
ejpam-2347	48	14	j	j	NOUN
ejpam-2347	48	15	the	the	DET
ejpam-2347	48	16	function	function	NOUN
ejpam-2347	48	17	f	f	PROPN
ejpam-2347	48	18	(	(	PUNCT
ejpam-2347	48	19	n	n	CCONJ
ejpam-2347	48	20	)	)	PUNCT
ejpam-2347	48	21	=	=	SYM
ejpam-2347	48	22	(	(	PUNCT
ejpam-2347	48	23	−1)n+1(n!)p	−1)n+1(n!)p	PUNCT
ejpam-2347	48	24	can	can	AUX
ejpam-2347	48	25	be	be	AUX
ejpam-2347	48	26	interpolated	interpolate	VERB
ejpam-2347	48	27	and	and	CCONJ
ejpam-2347	48	28	the	the	DET
ejpam-2347	48	29	p	p	ADJ
ejpam-2347	48	30	-	-	PUNCT
ejpam-2347	48	31	adic	adic	ADJ
ejpam-2347	48	32	gamma	gamma	NOUN
ejpam-2347	48	33	function	function	PROPN
ejpam-2347	48	34	γp	γp	PROPN
ejpam-2347	48	35	is	be	AUX
ejpam-2347	48	36	defined	define	VERB
ejpam-2347	48	37	as	as	SCONJ
ejpam-2347	48	38	follows	follow	VERB
ejpam-2347	48	39	:	:	PUNCT
ejpam-2347	48	40	definition	definition	NOUN
ejpam-2347	48	41	1	1	NUM
ejpam-2347	48	42	(	(	PUNCT
ejpam-2347	48	43	[	[	X
ejpam-2347	48	44	10	10	NUM
ejpam-2347	48	45	]	]	NUM
ejpam-2347	48	46	)	)	PUNCT
ejpam-2347	48	47	.	.	PUNCT
ejpam-2347	49	1	the	the	DET
ejpam-2347	49	2	p	p	ADJ
ejpam-2347	49	3	-	-	PUNCT
ejpam-2347	49	4	adic	adic	ADJ
ejpam-2347	49	5	gamma	gamma	NOUN
ejpam-2347	49	6	function	function	PROPN
ejpam-2347	49	7	γp	γp	PROPN
ejpam-2347	49	8	is	be	AUX
ejpam-2347	49	9	the	the	DET
ejpam-2347	49	10	continuous	continuous	ADJ
ejpam-2347	49	11	extension	extension	NOUN
ejpam-2347	49	12	to	to	ADP
ejpam-2347	49	13	zp	zp	PROPN
ejpam-2347	49	14	of	of	ADP
ejpam-2347	49	15	n	n	PROPN
ejpam-2347	49	16	7→	7→	PROPN
ejpam-2347	49	17	(	(	PUNCT
ejpam-2347	49	18	−1)n	−1)n	PROPN
ejpam-2347	49	19	∏	∏	PROPN
ejpam-2347	49	20	1≤	1≤	NUM
ejpam-2347	49	21	j	j	PROPN
ejpam-2347	49	22	<	<	X
ejpam-2347	49	23	n	n	PROPN
ejpam-2347	49	24	(	(	PUNCT
ejpam-2347	49	25	j	j	PROPN
ejpam-2347	49	26	,	,	PUNCT
ejpam-2347	49	27	p	p	NOUN
ejpam-2347	49	28	)	)	PUNCT
ejpam-2347	49	29	=	=	SYM
ejpam-2347	49	30	1	1	NUM
ejpam-2347	49	31	j(n≥	j(n≥	NOUN
ejpam-2347	49	32	2	2	NUM
ejpam-2347	49	33	)	)	PUNCT
ejpam-2347	49	34	.	.	PUNCT
ejpam-2347	50	1	moreover	moreover	ADV
ejpam-2347	50	2	,	,	PUNCT
ejpam-2347	50	3	γp	γp	PROPN
ejpam-2347	50	4	:	:	PUNCT
ejpam-2347	50	5	zp→	zp→	PUNCT
ejpam-2347	50	6	qp	qp	PROPN
ejpam-2347	50	7	function	function	PROPN
ejpam-2347	50	8	is	be	AUX
ejpam-2347	50	9	defined	define	VERB
ejpam-2347	50	10	by	by	ADP
ejpam-2347	50	11	γp(x	γp(x	PROPN
ejpam-2347	50	12	)	)	PUNCT
ejpam-2347	50	13	:	:	PUNCT
ejpam-2347	51	1	=	=	PUNCT
ejpam-2347	51	2	lim	lim	PROPN
ejpam-2347	51	3	n→x	n→x	NUM
ejpam-2347	51	4	(	(	PUNCT
ejpam-2347	51	5	−1)n	−1)n	PROPN
ejpam-2347	51	6	∏	∏	PROPN
ejpam-2347	51	7	1≤	1≤	NUM
ejpam-2347	51	8	j	j	PROPN
ejpam-2347	51	9	<	<	X
ejpam-2347	51	10	n	n	PROPN
ejpam-2347	51	11	(	(	PUNCT
ejpam-2347	51	12	j	j	PROPN
ejpam-2347	51	13	,	,	PUNCT
ejpam-2347	51	14	p	p	NOUN
ejpam-2347	51	15	)	)	PUNCT
ejpam-2347	51	16	=	=	SYM
ejpam-2347	51	17	1	1	NUM
ejpam-2347	51	18	j.	j.	NOUN
ejpam-2347	51	19	according	accord	VERB
ejpam-2347	51	20	the	the	DET
ejpam-2347	51	21	definition	definition	NOUN
ejpam-2347	51	22	of	of	ADP
ejpam-2347	51	23	p	p	NOUN
ejpam-2347	51	24	-	-	PUNCT
ejpam-2347	51	25	adic	adic	ADJ
ejpam-2347	51	26	factorial	factorial	NOUN
ejpam-2347	51	27	function	function	NOUN
ejpam-2347	51	28	we	we	PRON
ejpam-2347	51	29	conclude	conclude	VERB
ejpam-2347	51	30	that	that	SCONJ
ejpam-2347	51	31	:	:	PUNCT
ejpam-2347	51	32	corollary	corollary	ADJ
ejpam-2347	51	33	1	1	NUM
ejpam-2347	51	34	.	.	PUNCT
ejpam-2347	51	35	γp(n+	γp(n+	ADP
ejpam-2347	51	36	1	1	X
ejpam-2347	51	37	)	)	PUNCT
ejpam-2347	51	38	=	=	SYM
ejpam-2347	51	39	(	(	PUNCT
ejpam-2347	51	40	−1)n+1(n!)p	−1)n+1(n!)p	NUM
ejpam-2347	51	41	(	(	PUNCT
ejpam-2347	51	42	n	n	NOUN
ejpam-2347	51	43	∈	∈	PROPN
ejpam-2347	51	44	n	n	CCONJ
ejpam-2347	51	45	)	)	PUNCT
ejpam-2347	51	46	.	.	PUNCT
ejpam-2347	52	1	to	to	PART
ejpam-2347	52	2	prove	prove	VERB
ejpam-2347	52	3	our	our	PRON
ejpam-2347	52	4	results	result	NOUN
ejpam-2347	52	5	we	we	PRON
ejpam-2347	52	6	use	use	VERB
ejpam-2347	52	7	the	the	DET
ejpam-2347	52	8	following	follow	VERB
ejpam-2347	52	9	properties	property	NOUN
ejpam-2347	52	10	of	of	ADP
ejpam-2347	52	11	p	p	NOUN
ejpam-2347	52	12	-	-	PUNCT
ejpam-2347	52	13	adic	adic	ADJ
ejpam-2347	52	14	gamma	gamma	NOUN
ejpam-2347	52	15	function	function	NOUN
ejpam-2347	52	16	:	:	PUNCT
ejpam-2347	52	17	proposition	proposition	NOUN
ejpam-2347	52	18	1	1	NUM
ejpam-2347	52	19	(	(	PUNCT
ejpam-2347	52	20	[	[	X
ejpam-2347	52	21	12	12	NUM
ejpam-2347	52	22	]	]	PUNCT
ejpam-2347	52	23	)	)	PUNCT
ejpam-2347	52	24	.	.	PUNCT
ejpam-2347	53	1	let	let	VERB
ejpam-2347	53	2	p	p	PRON
ejpam-2347	53	3	6=	6=	ADP
ejpam-2347	53	4	2	2	NUM
ejpam-2347	53	5	.	.	PUNCT
ejpam-2347	54	1	then	then	ADV
ejpam-2347	54	2	γp	γp	PROPN
ejpam-2347	54	3	has	have	VERB
ejpam-2347	54	4	the	the	DET
ejpam-2347	54	5	following	follow	VERB
ejpam-2347	54	6	properties	property	NOUN
ejpam-2347	54	7	:	:	PUNCT
ejpam-2347	54	8	(	(	PUNCT
ejpam-2347	54	9	i	i	NOUN
ejpam-2347	54	10	)	)	PUNCT
ejpam-2347	54	11	for	for	ADP
ejpam-2347	54	12	all	all	DET
ejpam-2347	54	13	x	x	SYM
ejpam-2347	54	14	∈	∈	PROPN
ejpam-2347	54	15	zp	zp	PROPN
ejpam-2347	54	16	γp(x	γp(x	PUNCT
ejpam-2347	54	17	+	+	NOUN
ejpam-2347	54	18	1	1	X
ejpam-2347	54	19	)	)	PUNCT
ejpam-2347	54	20	=	=	SYM
ejpam-2347	54	21	hp(x)γp(x	hp(x)γp(x	PROPN
ejpam-2347	54	22	)	)	PUNCT
ejpam-2347	54	23	(	(	PUNCT
ejpam-2347	54	24	1	1	X
ejpam-2347	54	25	)	)	PUNCT
ejpam-2347	54	26	where	where	SCONJ
ejpam-2347	54	27	hp(x	hp(x	NOUN
ejpam-2347	54	28	)	)	PUNCT
ejpam-2347	54	29	:	:	PUNCT
ejpam-2347	54	30	=	=	SYM
ejpam-2347	54	31	¨	¨	NOUN
ejpam-2347	54	32	−x	−x	NOUN
ejpam-2347	54	33	if	if	SCONJ
ejpam-2347	54	34	|x	|x	NOUN
ejpam-2347	54	35	|p	|p	X
ejpam-2347	54	36	=	=	SYM
ejpam-2347	54	37	1	1	NUM
ejpam-2347	54	38	−1	−1	NOUN
ejpam-2347	54	39	if	if	SCONJ
ejpam-2347	54	40	|x	|x	PRON
ejpam-2347	54	41	|p	|p	VERB
ejpam-2347	54	42	<	<	X
ejpam-2347	54	43	1	1	NUM
ejpam-2347	54	44	(	(	PUNCT
ejpam-2347	54	45	ii	ii	NOUN
ejpam-2347	54	46	)	)	PUNCT
ejpam-2347	54	47	γp(0	γp(0	NOUN
ejpam-2347	54	48	)	)	PUNCT
ejpam-2347	54	49	=	=	SYM
ejpam-2347	54	50	1	1	NUM
ejpam-2347	54	51	,	,	PUNCT
ejpam-2347	54	52	γp(1	γp(1	NOUN
ejpam-2347	54	53	)	)	PUNCT
ejpam-2347	54	54	=	=	SYM
ejpam-2347	54	55	−1	−1	NOUN
ejpam-2347	54	56	,	,	PUNCT
ejpam-2347	54	57	γp(2	γp(2	NOUN
ejpam-2347	54	58	)	)	PUNCT
ejpam-2347	54	59	=	=	NOUN
ejpam-2347	54	60	1	1	X
ejpam-2347	54	61	.	.	X
ejpam-2347	55	1	for	for	ADP
ejpam-2347	55	2	all	all	DET
ejpam-2347	55	3	x	x	SYM
ejpam-2347	55	4	∈	∈	NOUN
ejpam-2347	55	5	zp	zp	NOUN
ejpam-2347	55	6	we	we	PRON
ejpam-2347	55	7	have	have	VERB
ejpam-2347	55	8	�	�	PROPN
ejpam-2347	55	9	�	�	PROPN
ejpam-2347	55	10	γp(x	γp(x	PART
ejpam-2347	55	11	)	)	PUNCT
ejpam-2347	55	12	�	�	PROPN
ejpam-2347	55	13	�	�	PROPN
ejpam-2347	55	14	p	p	NOUN
ejpam-2347	55	15	=	=	SYM
ejpam-2347	55	16	1	1	NUM
ejpam-2347	55	17	(	(	PUNCT
ejpam-2347	55	18	iii	iii	NOUN
ejpam-2347	55	19	)	)	PUNCT
ejpam-2347	55	20	for	for	ADP
ejpam-2347	55	21	all	all	DET
ejpam-2347	55	22	x	x	SYM
ejpam-2347	55	23	,	,	PUNCT
ejpam-2347	55	24	y	y	PROPN
ejpam-2347	55	25	∈	∈	PROPN
ejpam-2347	55	26	zp	zp	PROPN
ejpam-2347	55	27	�	�	PROPN
ejpam-2347	55	28	�	�	PROPN
ejpam-2347	55	29	γp(x)−	γp(x)−	PROPN
ejpam-2347	55	30	γp(y	γp(y	PUNCT
ejpam-2347	55	31	)	)	PUNCT
ejpam-2347	55	32	�	�	PROPN
ejpam-2347	55	33	�	�	PROPN
ejpam-2347	55	34	p	p	PROPN
ejpam-2347	55	35	≤	≤	PROPN
ejpam-2347	55	36	�	�	PROPN
ejpam-2347	55	37	�	�	PROPN
ejpam-2347	55	38	x	x	PROPN
ejpam-2347	55	39	−	−	PROPN
ejpam-2347	55	40	y	y	PROPN
ejpam-2347	55	41	�	�	PROPN
ejpam-2347	55	42	�	�	PROPN
ejpam-2347	55	43	p	p	PROPN
ejpam-2347	55	44	.	.	PUNCT
ejpam-2347	56	1	(	(	PUNCT
ejpam-2347	56	2	2	2	X
ejpam-2347	56	3	)	)	PUNCT
ejpam-2347	56	4	h.	h.	PROPN
ejpam-2347	56	5	menken	menken	PROPN
ejpam-2347	56	6	,	,	PUNCT
ejpam-2347	56	7	ö.	ö.	VERB
ejpam-2347	56	8	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	56	9	/	/	SYM
ejpam-2347	56	10	eur	eur	PROPN
ejpam-2347	56	11	.	.	PUNCT
ejpam-2347	57	1	j.	j.	PROPN
ejpam-2347	57	2	pure	pure	PROPN
ejpam-2347	57	3	appl	appl	PROPN
ejpam-2347	57	4	.	.	PROPN
ejpam-2347	57	5	math	math	PROPN
ejpam-2347	57	6	,	,	PUNCT
ejpam-2347	57	7	8	8	NUM
ejpam-2347	57	8	(	(	PUNCT
ejpam-2347	57	9	2015	2015	NUM
ejpam-2347	57	10	)	)	PUNCT
ejpam-2347	57	11	,	,	PUNCT
ejpam-2347	57	12	214	214	NUM
ejpam-2347	57	13	-	-	SYM
ejpam-2347	57	14	231	231	NUM
ejpam-2347	57	15	217	217	NUM
ejpam-2347	57	16	also	also	ADV
ejpam-2347	57	17	,	,	PUNCT
ejpam-2347	57	18	the	the	DET
ejpam-2347	57	19	properties	property	NOUN
ejpam-2347	57	20	(	(	PUNCT
ejpam-2347	57	21	i	i	NOUN
ejpam-2347	57	22	)	)	PUNCT
ejpam-2347	57	23	and	and	CCONJ
ejpam-2347	57	24	(	(	PUNCT
ejpam-2347	57	25	ii	ii	NOUN
ejpam-2347	57	26	)	)	PUNCT
ejpam-2347	57	27	hold	hold	VERB
ejpam-2347	57	28	for	for	ADP
ejpam-2347	57	29	p	p	NOUN
ejpam-2347	57	30	=	=	SYM
ejpam-2347	57	31	2	2	NUM
ejpam-2347	57	32	,	,	PUNCT
ejpam-2347	57	33	and	and	CCONJ
ejpam-2347	57	34	the	the	DET
ejpam-2347	57	35	instead	instead	ADV
ejpam-2347	57	36	of	of	ADP
ejpam-2347	57	37	(	(	PUNCT
ejpam-2347	57	38	iii	iii	X
ejpam-2347	57	39	)	)	PUNCT
ejpam-2347	57	40	the	the	DET
ejpam-2347	57	41	relations	relation	NOUN
ejpam-2347	57	42	�	�	PROPN
ejpam-2347	57	43	�	�	PROPN
ejpam-2347	57	44	γ2(x)−	γ2(x)−	PROPN
ejpam-2347	57	45	γ2(y	γ2(y	PROPN
ejpam-2347	57	46	)	)	PUNCT
ejpam-2347	57	47	�	�	PROPN
ejpam-2347	57	48	�	�	PROPN
ejpam-2347	57	49	2	2	NUM
ejpam-2347	57	50	≤	≤	PROPN
ejpam-2347	57	51	�	�	PROPN
ejpam-2347	57	52	�	�	PROPN
ejpam-2347	57	53	x	x	PROPN
ejpam-2347	57	54	−	−	PROPN
ejpam-2347	57	55	y	y	PROPN
ejpam-2347	57	56	�	�	PROPN
ejpam-2347	57	57	�	�	PROPN
ejpam-2347	57	58	2	2	NUM
ejpam-2347	57	59	(	(	PUNCT
ejpam-2347	57	60	x	x	X
ejpam-2347	57	61	,	,	PUNCT
ejpam-2347	57	62	y	y	PROPN
ejpam-2347	57	63	∈	∈	PROPN
ejpam-2347	57	64	z2	z2	PROPN
ejpam-2347	57	65	,	,	PUNCT
ejpam-2347	57	66	�	�	PROPN
ejpam-2347	57	67	�	�	PROPN
ejpam-2347	57	68	x	x	PROPN
ejpam-2347	57	69	−	−	PROPN
ejpam-2347	57	70	y	y	PROPN
ejpam-2347	57	71	�	�	PROPN
ejpam-2347	57	72	�	�	PROPN
ejpam-2347	57	73	2	2	NUM
ejpam-2347	57	74	6=	6=	SYM
ejpam-2347	57	75	1	1	NUM
ejpam-2347	57	76	4	4	NUM
ejpam-2347	57	77	)	)	PUNCT
ejpam-2347	57	78	�	�	PROPN
ejpam-2347	57	79	�	�	PROPN
ejpam-2347	57	80	γ2(x)−	γ2(x)−	PROPN
ejpam-2347	57	81	γ2(y	γ2(y	PROPN
ejpam-2347	57	82	)	)	PUNCT
ejpam-2347	57	83	�	�	PROPN
ejpam-2347	57	84	�	�	PROPN
ejpam-2347	57	85	2	2	NUM
ejpam-2347	57	86	≤	≤	NUM
ejpam-2347	57	87	2	2	NUM
ejpam-2347	57	88	�	�	PROPN
ejpam-2347	57	89	�	�	PROPN
ejpam-2347	57	90	x	x	PROPN
ejpam-2347	57	91	−	−	PROPN
ejpam-2347	57	92	y	y	PROPN
ejpam-2347	57	93	�	�	PROPN
ejpam-2347	57	94	�	�	PROPN
ejpam-2347	57	95	2	2	NUM
ejpam-2347	57	96	(	(	PUNCT
ejpam-2347	57	97	x	x	X
ejpam-2347	57	98	,	,	PUNCT
ejpam-2347	57	99	y	y	PROPN
ejpam-2347	57	100	∈	∈	PROPN
ejpam-2347	57	101	z2	z2	PROPN
ejpam-2347	57	102	,	,	PUNCT
ejpam-2347	57	103	�	�	PROPN
ejpam-2347	57	104	�	�	PROPN
ejpam-2347	57	105	x	x	PROPN
ejpam-2347	57	106	−	−	PROPN
ejpam-2347	57	107	y	y	PROPN
ejpam-2347	57	108	�	�	PROPN
ejpam-2347	57	109	�	�	PROPN
ejpam-2347	57	110	2	2	NUM
ejpam-2347	57	111	=	=	SYM
ejpam-2347	57	112	1	1	NUM
ejpam-2347	57	113	4	4	NUM
ejpam-2347	57	114	)	)	PUNCT
ejpam-2347	57	115	hold	hold	VERB
ejpam-2347	57	116	.	.	PUNCT
ejpam-2347	58	1	proposition	proposition	NOUN
ejpam-2347	58	2	2	2	NUM
ejpam-2347	58	3	(	(	PUNCT
ejpam-2347	58	4	[	[	X
ejpam-2347	58	5	12	12	NUM
ejpam-2347	58	6	]	]	NUM
ejpam-2347	58	7	)	)	PUNCT
ejpam-2347	58	8	.	.	PUNCT
ejpam-2347	59	1	a	a	DET
ejpam-2347	59	2	formula	formula	NOUN
ejpam-2347	59	3	for	for	ADP
ejpam-2347	59	4	γp(−n	γp(−n	NOUN
ejpam-2347	59	5	)	)	PUNCT
ejpam-2347	59	6	(	(	PUNCT
ejpam-2347	59	7	n	n	CCONJ
ejpam-2347	59	8	∈	∈	PROPN
ejpam-2347	59	9	n	n	CCONJ
ejpam-2347	59	10	)	)	PUNCT
ejpam-2347	59	11	is	be	AUX
ejpam-2347	59	12	given	give	VERB
ejpam-2347	59	13	by	by	ADP
ejpam-2347	59	14	γp(−n	γp(−n	NOUN
ejpam-2347	59	15	)	)	PUNCT
ejpam-2347	59	16	=	=	SYM
ejpam-2347	59	17	(	(	PUNCT
ejpam-2347	59	18	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	59	19	�	�	PROPN
ejpam-2347	59	20	n	n	CCONJ
ejpam-2347	59	21	p	p	PROPN
ejpam-2347	59	22	�	�	PROPN
ejpam-2347	59	23	(	(	PUNCT
ejpam-2347	59	24	γp(n+	γp(n+	PROPN
ejpam-2347	59	25	1))−1	1))−1	NUM
ejpam-2347	59	26	.	.	PUNCT
ejpam-2347	60	1	(	(	PUNCT
ejpam-2347	60	2	3	3	X
ejpam-2347	60	3	)	)	PUNCT
ejpam-2347	60	4	proposition	proposition	NOUN
ejpam-2347	60	5	3	3	NUM
ejpam-2347	60	6	(	(	PUNCT
ejpam-2347	60	7	[	[	X
ejpam-2347	60	8	7	7	NUM
ejpam-2347	60	9	,	,	PUNCT
ejpam-2347	60	10	12	12	NUM
ejpam-2347	60	11	]	]	PUNCT
ejpam-2347	60	12	)	)	PUNCT
ejpam-2347	60	13	.	.	PUNCT
ejpam-2347	61	1	if	if	SCONJ
ejpam-2347	61	2	p	p	PROPN
ejpam-2347	61	3	6=	6=	NUM
ejpam-2347	61	4	2	2	NUM
ejpam-2347	61	5	then	then	ADV
ejpam-2347	61	6	γp(x)γp(1−	γp(x)γp(1−	PROPN
ejpam-2347	61	7	x	x	SYM
ejpam-2347	61	8	)	)	PUNCT
ejpam-2347	62	1	=	=	SYM
ejpam-2347	62	2	(	(	PUNCT
ejpam-2347	62	3	−1)ℓ(x	−1)ℓ(x	NOUN
ejpam-2347	62	4	)	)	PUNCT
ejpam-2347	62	5	(	(	PUNCT
ejpam-2347	62	6	x	x	SYM
ejpam-2347	62	7	∈	∈	PROPN
ejpam-2347	62	8	zp	zp	X
ejpam-2347	62	9	)	)	PUNCT
ejpam-2347	62	10	(	(	PUNCT
ejpam-2347	62	11	4	4	NUM
ejpam-2347	62	12	)	)	PUNCT
ejpam-2347	62	13	and	and	CCONJ
ejpam-2347	62	14	for	for	ADP
ejpam-2347	62	15	p	p	NOUN
ejpam-2347	62	16	=	=	SYM
ejpam-2347	62	17	2	2	NUM
ejpam-2347	62	18	γp(x)γp(1−	γp(x)γp(1−	PROPN
ejpam-2347	62	19	x	x	NOUN
ejpam-2347	62	20	)	)	PUNCT
ejpam-2347	62	21	=	=	SYM
ejpam-2347	62	22	(	(	PUNCT
ejpam-2347	62	23	−1)σ1(x)+1	−1)σ1(x)+1	PROPN
ejpam-2347	62	24	(	(	PUNCT
ejpam-2347	62	25	x	x	PROPN
ejpam-2347	62	26	∈	∈	PROPN
ejpam-2347	62	27	z2	z2	PROPN
ejpam-2347	62	28	)	)	PUNCT
ejpam-2347	62	29	(	(	PUNCT
ejpam-2347	62	30	5	5	X
ejpam-2347	62	31	)	)	PUNCT
ejpam-2347	62	32	where	where	SCONJ
ejpam-2347	62	33	ℓ	ℓ	NOUN
ejpam-2347	62	34	:	:	PUNCT
ejpam-2347	62	35	zp	zp	PROPN
ejpam-2347	62	36	→	→	SYM
ejpam-2347	62	37	�	�	PROPN
ejpam-2347	62	38	1,2	1,2	NUM
ejpam-2347	62	39	,	,	PUNCT
ejpam-2347	62	40	.	.	PUNCT
ejpam-2347	62	41	.	.	PUNCT
ejpam-2347	62	42	.	.	PUNCT
ejpam-2347	63	1	,	,	PUNCT
ejpam-2347	63	2	p	p	NOUN
ejpam-2347	63	3	assigns	assign	VERB
ejpam-2347	63	4	to	to	ADP
ejpam-2347	63	5	x	x	PUNCT
ejpam-2347	63	6	∈	∈	PROPN
ejpam-2347	63	7	zp	zp	NOUN
ejpam-2347	63	8	its	its	PRON
ejpam-2347	63	9	residue	residue	NOUN
ejpam-2347	63	10	∈	∈	PROPN
ejpam-2347	63	11	�	�	NOUN
ejpam-2347	63	12	1,2	1,2	NUM
ejpam-2347	63	13	,	,	PUNCT
ejpam-2347	63	14	.	.	PUNCT
ejpam-2347	63	15	.	.	PUNCT
ejpam-2347	64	1	.	.	PUNCT
ejpam-2347	65	1	,	,	PUNCT
ejpam-2347	65	2	p	p	X
ejpam-2347	65	3	modulo	modulo	ADJ
ejpam-2347	65	4	pzp	pzp	NOUN
ejpam-2347	65	5	and	and	CCONJ
ejpam-2347	65	6	where	where	SCONJ
ejpam-2347	65	7	σ1	σ1	PROPN
ejpam-2347	65	8	is	be	AUX
ejpam-2347	65	9	defined	define	VERB
ejpam-2347	65	10	by	by	ADP
ejpam-2347	65	11	the	the	DET
ejpam-2347	65	12	formula	formula	NOUN
ejpam-2347	65	13	σ1	σ1	PROPN
ejpam-2347	65	14	(	(	PUNCT
ejpam-2347	65	15	∞	∞	PROPN
ejpam-2347	65	16	∑	∑	PUNCT
ejpam-2347	65	17	j=0	j=0	PROPN
ejpam-2347	65	18	a	a	DET
ejpam-2347	65	19	j2	j2	PROPN
ejpam-2347	65	20	j	j	PROPN
ejpam-2347	65	21	)	)	PUNCT
ejpam-2347	66	1	=	=	NOUN
ejpam-2347	66	2	a1	a1	NOUN
ejpam-2347	66	3	corollary	corollary	NOUN
ejpam-2347	66	4	2	2	NUM
ejpam-2347	66	5	(	(	PUNCT
ejpam-2347	66	6	[	[	X
ejpam-2347	66	7	12	12	NUM
ejpam-2347	66	8	]	]	PUNCT
ejpam-2347	66	9	)	)	PUNCT
ejpam-2347	66	10	.	.	PUNCT
ejpam-2347	67	1	let	let	VERB
ejpam-2347	67	2	p	p	PRON
ejpam-2347	67	3	6=	6=	ADP
ejpam-2347	67	4	2	2	NUM
ejpam-2347	67	5	.	.	PUNCT
ejpam-2347	68	1	we	we	PRON
ejpam-2347	68	2	get	get	VERB
ejpam-2347	68	3	γp	γp	NOUN
ejpam-2347	68	4	(	(	PUNCT
ejpam-2347	68	5	1	1	NUM
ejpam-2347	68	6	2	2	NUM
ejpam-2347	68	7	)	)	PUNCT
ejpam-2347	68	8	2	2	NUM
ejpam-2347	68	9	=	=	SYM
ejpam-2347	68	10	(	(	PUNCT
ejpam-2347	68	11	−1	−1	NOUN
ejpam-2347	68	12	)	)	PUNCT
ejpam-2347	68	13	ℓ	ℓ	NOUN
ejpam-2347	68	14	(	(	PUNCT
ejpam-2347	68	15	1	1	NUM
ejpam-2347	68	16	2	2	NUM
ejpam-2347	68	17	)	)	PUNCT
ejpam-2347	68	18	(	(	PUNCT
ejpam-2347	68	19	6	6	X
ejpam-2347	68	20	)	)	PUNCT
ejpam-2347	68	21	now	now	ADV
ejpam-2347	68	22	ℓ(1	ℓ(1	ADP
ejpam-2347	68	23	2	2	X
ejpam-2347	68	24	)	)	PUNCT
ejpam-2347	68	25	=	=	SYM
ejpam-2347	68	26	ℓ	ℓ	PROPN
ejpam-2347	68	27	(	(	PUNCT
ejpam-2347	68	28	1	1	NUM
ejpam-2347	68	29	2(p+	2(p+	NUM
ejpam-2347	68	30	1	1	NUM
ejpam-2347	68	31	)	)	PUNCT
ejpam-2347	68	32	)	)	PUNCT
ejpam-2347	68	33	=	=	SYM
ejpam-2347	69	1	1	1	NUM
ejpam-2347	69	2	2(p+	2(p+	NUM
ejpam-2347	69	3	1	1	NUM
ejpam-2347	69	4	)	)	PUNCT
ejpam-2347	70	1	so	so	SCONJ
ejpam-2347	70	2	that	that	SCONJ
ejpam-2347	70	3	γp	γp	NOUN
ejpam-2347	70	4	(	(	PUNCT
ejpam-2347	70	5	1	1	NUM
ejpam-2347	70	6	2	2	NUM
ejpam-2347	70	7	)	)	PUNCT
ejpam-2347	70	8	2	2	NUM
ejpam-2347	70	9	=	=	SYM
ejpam-2347	70	10	¨	¨	NOUN
ejpam-2347	70	11	1	1	NUM
ejpam-2347	70	12	if	if	SCONJ
ejpam-2347	70	13	p	p	PRON
ejpam-2347	70	14	≡	≡	PROPN
ejpam-2347	70	15	3	3	NUM
ejpam-2347	70	16	(	(	PUNCT
ejpam-2347	70	17	mod	mod	NOUN
ejpam-2347	70	18	4	4	NUM
ejpam-2347	70	19	)	)	PUNCT
ejpam-2347	70	20	−1	−1	NOUN
ejpam-2347	70	21	if	if	SCONJ
ejpam-2347	70	22	p	p	PRON
ejpam-2347	70	23	≡	≡	PROPN
ejpam-2347	70	24	1	1	NUM
ejpam-2347	70	25	(	(	PUNCT
ejpam-2347	70	26	mod	mod	NOUN
ejpam-2347	70	27	4	4	NUM
ejpam-2347	70	28	)	)	PUNCT
ejpam-2347	70	29	(	(	PUNCT
ejpam-2347	70	30	7	7	X
ejpam-2347	70	31	)	)	PUNCT
ejpam-2347	70	32	proposition	proposition	NOUN
ejpam-2347	70	33	4	4	NUM
ejpam-2347	70	34	(	(	PUNCT
ejpam-2347	70	35	[	[	X
ejpam-2347	70	36	12	12	NUM
ejpam-2347	70	37	]	]	PUNCT
ejpam-2347	70	38	)	)	PUNCT
ejpam-2347	70	39	.	.	PUNCT
ejpam-2347	71	1	let	let	VERB
ejpam-2347	71	2	n	n	PRON
ejpam-2347	71	3	∈	∈	PROPN
ejpam-2347	71	4	n	n	ADV
ejpam-2347	71	5	and	and	CCONJ
ejpam-2347	71	6	let	let	VERB
ejpam-2347	71	7	sn	sn	PROPN
ejpam-2347	71	8	be	be	AUX
ejpam-2347	71	9	sum	sum	NOUN
ejpam-2347	71	10	of	of	ADP
ejpam-2347	71	11	the	the	DET
ejpam-2347	71	12	digits	digit	NOUN
ejpam-2347	71	13	of	of	ADP
ejpam-2347	71	14	n	n	PROPN
ejpam-2347	71	15	=	=	SYM
ejpam-2347	71	16	s	s	PROPN
ejpam-2347	71	17	∑	∑	PUNCT
ejpam-2347	71	18	j=0	j=0	PROPN
ejpam-2347	71	19	a	a	DET
ejpam-2347	71	20	j	j	PROPN
ejpam-2347	71	21	p	p	X
ejpam-2347	71	22	j	j	PROPN
ejpam-2347	71	23	(	(	PUNCT
ejpam-2347	71	24	as	as	ADP
ejpam-2347	71	25	6=	6=	NUM
ejpam-2347	71	26	0	0	NUM
ejpam-2347	71	27	)	)	PUNCT
ejpam-2347	71	28	in	in	ADP
ejpam-2347	71	29	base	base	NOUN
ejpam-2347	72	1	p.	p.	NOUN
ejpam-2347	72	2	then	then	ADV
ejpam-2347	72	3	(	(	PUNCT
ejpam-2347	72	4	i	i	NOUN
ejpam-2347	72	5	)	)	PUNCT
ejpam-2347	72	6	γp(n+	γp(n+	ADP
ejpam-2347	73	1	1	1	X
ejpam-2347	73	2	)	)	PUNCT
ejpam-2347	73	3	=	=	PRON
ejpam-2347	73	4	(	(	PUNCT
ejpam-2347	73	5	−1)n+1	−1)n+1	NOUN
ejpam-2347	73	6	n	n	X
ejpam-2347	73	7	!	!	PUNCT
ejpam-2347	73	8	�	�	PROPN
ejpam-2347	73	9	n	n	CCONJ
ejpam-2347	73	10	p	p	PROPN
ejpam-2347	73	11	�	�	PROPN
ejpam-2347	73	12	!	!	PUNCT
ejpam-2347	74	1	p	p	X
ejpam-2347	74	2	[	[	PUNCT
ejpam-2347	74	3	n	n	NOUN
ejpam-2347	74	4	p	p	NOUN
ejpam-2347	74	5	]	]	X
ejpam-2347	74	6	(	(	PUNCT
ejpam-2347	74	7	ii	ii	NOUN
ejpam-2347	74	8	)	)	PUNCT
ejpam-2347	74	9	γp(p	γp(p	NOUN
ejpam-2347	74	10	n	n	CCONJ
ejpam-2347	74	11	)	)	PUNCT
ejpam-2347	75	1	=	=	SYM
ejpam-2347	75	2	(	(	PUNCT
ejpam-2347	75	3	−1)p	−1)p	X
ejpam-2347	75	4	pn	pn	PROPN
ejpam-2347	75	5	!	!	PROPN
ejpam-2347	75	6	pn−1!ppn−1	pn−1!ppn−1	PROPN
ejpam-2347	75	7	(	(	PUNCT
ejpam-2347	75	8	iii	iii	NOUN
ejpam-2347	75	9	)	)	PUNCT
ejpam-2347	75	10	n!=	n!=	PROPN
ejpam-2347	75	11	(	(	PUNCT
ejpam-2347	75	12	−1)n+1−s(−p)(n−sn)/(p−1	−1)n+1−s(−p)(n−sn)/(p−1	NOUN
ejpam-2347	75	13	)	)	PUNCT
ejpam-2347	75	14	n	n	CCONJ
ejpam-2347	76	1	π	π	PROPN
ejpam-2347	76	2	j=0	j=0	PROPN
ejpam-2347	76	3	γp	γp	PROPN
ejpam-2347	76	4	�	�	PROPN
ejpam-2347	76	5	�	�	PROPN
ejpam-2347	76	6	n	n	CCONJ
ejpam-2347	76	7	p	p	PROPN
ejpam-2347	76	8	j	j	PROPN
ejpam-2347	76	9	�	�	PROPN
ejpam-2347	76	10	+	+	CCONJ
ejpam-2347	76	11	1	1	NUM
ejpam-2347	76	12	�	�	PROPN
ejpam-2347	76	13	h.	h.	PROPN
ejpam-2347	76	14	menken	menken	PROPN
ejpam-2347	76	15	,	,	PUNCT
ejpam-2347	76	16	ö.	ö.	VERB
ejpam-2347	76	17	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	76	18	/	/	SYM
ejpam-2347	76	19	eur	eur	PROPN
ejpam-2347	76	20	.	.	PUNCT
ejpam-2347	77	1	j.	j.	PROPN
ejpam-2347	77	2	pure	pure	PROPN
ejpam-2347	77	3	appl	appl	PROPN
ejpam-2347	77	4	.	.	PROPN
ejpam-2347	77	5	math	math	PROPN
ejpam-2347	77	6	,	,	PUNCT
ejpam-2347	77	7	8	8	NUM
ejpam-2347	77	8	(	(	PUNCT
ejpam-2347	77	9	2015	2015	NUM
ejpam-2347	77	10	)	)	PUNCT
ejpam-2347	77	11	,	,	PUNCT
ejpam-2347	77	12	214	214	NUM
ejpam-2347	77	13	-	-	SYM
ejpam-2347	77	14	231	231	NUM
ejpam-2347	77	15	218	218	NUM
ejpam-2347	77	16	(	(	PUNCT
ejpam-2347	77	17	iv	iv	NOUN
ejpam-2347	77	18	)	)	PUNCT
ejpam-2347	77	19	pn!=	pn!=	NOUN
ejpam-2347	77	20	(	(	PUNCT
ejpam-2347	77	21	−1)p(−p)(p	−1)p(−p)(p	NOUN
ejpam-2347	77	22	n−1)/(p−1	n−1)/(p−1	PROPN
ejpam-2347	77	23	)	)	PUNCT
ejpam-2347	77	24	n	n	PROPN
ejpam-2347	77	25	π	π	PROPN
ejpam-2347	77	26	j=0	j=0	PROPN
ejpam-2347	77	27	γp	γp	PROPN
ejpam-2347	77	28	�	�	PROPN
ejpam-2347	77	29	p	p	PROPN
ejpam-2347	77	30	j	j	PROPN
ejpam-2347	77	31	�	�	PROPN
ejpam-2347	77	32	.	.	PUNCT
ejpam-2347	78	1	the	the	DET
ejpam-2347	78	2	p	p	ADJ
ejpam-2347	78	3	-	-	PUNCT
ejpam-2347	78	4	adic	adic	ADJ
ejpam-2347	78	5	gamma	gamma	NOUN
ejpam-2347	78	6	function	function	NOUN
ejpam-2347	78	7	have	have	AUX
ejpam-2347	78	8	been	be	AUX
ejpam-2347	78	9	considered	consider	VERB
ejpam-2347	78	10	by	by	ADP
ejpam-2347	78	11	many	many	ADJ
ejpam-2347	78	12	authors	author	NOUN
ejpam-2347	78	13	(	(	PUNCT
ejpam-2347	78	14	see	see	VERB
ejpam-2347	78	15	[	[	X
ejpam-2347	78	16	3–10	3–10	NOUN
ejpam-2347	78	17	,	,	PUNCT
ejpam-2347	78	18	13	13	NUM
ejpam-2347	78	19	]	]	NUM
ejpam-2347	78	20	)	)	PUNCT
ejpam-2347	78	21	.	.	PUNCT
ejpam-2347	79	1	we	we	PRON
ejpam-2347	79	2	note	note	VERB
ejpam-2347	79	3	that	that	SCONJ
ejpam-2347	79	4	another	another	DET
ejpam-2347	79	5	p	p	ADJ
ejpam-2347	79	6	-	-	PUNCT
ejpam-2347	79	7	adic	adic	ADJ
ejpam-2347	79	8	analogue	analogue	NOUN
ejpam-2347	79	9	of	of	ADP
ejpam-2347	79	10	classical	classical	ADJ
ejpam-2347	79	11	gamma	gamma	NOUN
ejpam-2347	79	12	function	function	NOUN
ejpam-2347	79	13	was	be	AUX
ejpam-2347	79	14	constructed	construct	VERB
ejpam-2347	79	15	by	by	ADP
ejpam-2347	79	16	g.	g.	PROPN
ejpam-2347	79	17	overholtzer	overholtzer	PROPN
ejpam-2347	80	1	[	[	X
ejpam-2347	80	2	11	11	NUM
ejpam-2347	80	3	]	]	PUNCT
ejpam-2347	80	4	,	,	PUNCT
ejpam-2347	80	5	but	but	CCONJ
ejpam-2347	80	6	we	we	PRON
ejpam-2347	80	7	consider	consider	VERB
ejpam-2347	80	8	morita	morita	PROPN
ejpam-2347	80	9	’s	’s	PART
ejpam-2347	80	10	p	p	ADJ
ejpam-2347	80	11	-	-	PUNCT
ejpam-2347	80	12	adic	adic	ADJ
ejpam-2347	80	13	gamma	gamma	NOUN
ejpam-2347	80	14	function	function	NOUN
ejpam-2347	80	15	.	.	PUNCT
ejpam-2347	81	1	in	in	ADP
ejpam-2347	81	2	1980	1980	NUM
ejpam-2347	81	3	the	the	DET
ejpam-2347	81	4	p	p	NOUN
ejpam-2347	81	5	-	-	PUNCT
ejpam-2347	81	6	adic	adic	ADJ
ejpam-2347	81	7	beta	beta	NOUN
ejpam-2347	81	8	function	function	NOUN
ejpam-2347	81	9	is	be	AUX
ejpam-2347	81	10	used	use	VERB
ejpam-2347	81	11	in	in	ADP
ejpam-2347	81	12	dwork	dwork	ADJ
ejpam-2347	81	13	cohomology	cohomology	NOUN
ejpam-2347	81	14	and	and	CCONJ
ejpam-2347	81	15	an	an	DET
ejpam-2347	81	16	cohomological	cohomological	ADJ
ejpam-2347	81	17	interpretation	interpretation	NOUN
ejpam-2347	81	18	of	of	ADP
ejpam-2347	81	19	p	p	NOUN
ejpam-2347	81	20	-	-	PUNCT
ejpam-2347	81	21	adic	adic	ADJ
ejpam-2347	81	22	beta	beta	NOUN
ejpam-2347	81	23	function	function	NOUN
ejpam-2347	81	24	is	be	AUX
ejpam-2347	81	25	given	give	VERB
ejpam-2347	81	26	by	by	ADP
ejpam-2347	81	27	m.	m.	NOUN
ejpam-2347	81	28	boyarsky	boyarsky	NOUN
ejpam-2347	82	1	[	[	X
ejpam-2347	82	2	4	4	NUM
ejpam-2347	82	3	]	]	PUNCT
ejpam-2347	82	4	.	.	PUNCT
ejpam-2347	83	1	in	in	ADP
ejpam-2347	83	2	2006	2006	NUM
ejpam-2347	83	3	f.	f.	PROPN
ejpam-2347	83	4	baldassarri	baldassarri	PROPN
ejpam-2347	83	5	[	[	X
ejpam-2347	83	6	2	2	NUM
ejpam-2347	83	7	]	]	PUNCT
ejpam-2347	83	8	considered	consider	VERB
ejpam-2347	83	9	two	two	NUM
ejpam-2347	83	10	constructions	construction	NOUN
ejpam-2347	83	11	of	of	ADP
ejpam-2347	83	12	the	the	DET
ejpam-2347	83	13	p	p	NOUN
ejpam-2347	83	14	-	-	PUNCT
ejpam-2347	83	15	adic	adic	ADJ
ejpam-2347	83	16	beta	beta	NOUN
ejpam-2347	83	17	functions	function	NOUN
ejpam-2347	83	18	as	as	ADP
ejpam-2347	83	19	the	the	DET
ejpam-2347	83	20	p	p	NOUN
ejpam-2347	83	21	-	-	PUNCT
ejpam-2347	83	22	adic	adic	ADJ
ejpam-2347	83	23	etale	etale	NOUN
ejpam-2347	83	24	and	and	CCONJ
ejpam-2347	83	25	p	p	ADJ
ejpam-2347	83	26	-	-	PUNCT
ejpam-2347	83	27	adic	adic	ADJ
ejpam-2347	83	28	crystalline	crystalline	NOUN
ejpam-2347	83	29	beta	beta	NOUN
ejpam-2347	83	30	functions	function	NOUN
ejpam-2347	83	31	.	.	PUNCT
ejpam-2347	84	1	also	also	ADV
ejpam-2347	84	2	,	,	PUNCT
ejpam-2347	84	3	some	some	DET
ejpam-2347	84	4	comparisons	comparison	NOUN
ejpam-2347	84	5	between	between	ADP
ejpam-2347	84	6	the	the	DET
ejpam-2347	84	7	p	p	NOUN
ejpam-2347	84	8	-	-	PUNCT
ejpam-2347	84	9	adic	adic	ADJ
ejpam-2347	84	10	etale	etale	NOUN
ejpam-2347	84	11	and	and	CCONJ
ejpam-2347	84	12	p	p	ADJ
ejpam-2347	84	13	-	-	PUNCT
ejpam-2347	84	14	adic	adic	ADJ
ejpam-2347	84	15	crystalline	crystalline	NOUN
ejpam-2347	84	16	beta	beta	NOUN
ejpam-2347	84	17	functions	function	NOUN
ejpam-2347	84	18	with	with	ADP
ejpam-2347	84	19	relations	relation	NOUN
ejpam-2347	84	20	via	via	ADP
ejpam-2347	84	21	fontaine	fontaine	PROPN
ejpam-2347	84	22	’s	’s	PART
ejpam-2347	84	23	periods	period	NOUN
ejpam-2347	84	24	are	be	AUX
ejpam-2347	84	25	given	give	VERB
ejpam-2347	84	26	.	.	PUNCT
ejpam-2347	85	1	in	in	ADP
ejpam-2347	85	2	the	the	DET
ejpam-2347	85	3	present	present	ADJ
ejpam-2347	85	4	work	work	NOUN
ejpam-2347	85	5	we	we	PRON
ejpam-2347	85	6	study	study	VERB
ejpam-2347	85	7	a	a	DET
ejpam-2347	85	8	p	p	ADJ
ejpam-2347	85	9	-	-	PUNCT
ejpam-2347	85	10	adic	adic	ADJ
ejpam-2347	85	11	analogue	analogue	NOUN
ejpam-2347	85	12	of	of	ADP
ejpam-2347	85	13	classical	classical	ADJ
ejpam-2347	85	14	beta	beta	NOUN
ejpam-2347	85	15	function	function	NOUN
ejpam-2347	85	16	by	by	ADP
ejpam-2347	85	17	using	use	VERB
ejpam-2347	85	18	morita	morita	PROPN
ejpam-2347	85	19	’s	’s	PART
ejpam-2347	85	20	p	p	ADJ
ejpam-2347	85	21	-	-	PUNCT
ejpam-2347	85	22	adic	adic	ADJ
ejpam-2347	85	23	gamma	gamma	NOUN
ejpam-2347	85	24	function	function	NOUN
ejpam-2347	85	25	,	,	PUNCT
ejpam-2347	85	26	and	and	CCONJ
ejpam-2347	85	27	we	we	PRON
ejpam-2347	85	28	obtain	obtain	VERB
ejpam-2347	85	29	some	some	DET
ejpam-2347	85	30	elemantary	elemantary	ADJ
ejpam-2347	85	31	properties	property	NOUN
ejpam-2347	85	32	of	of	ADP
ejpam-2347	85	33	the	the	DET
ejpam-2347	85	34	p	p	NOUN
ejpam-2347	85	35	-	-	PUNCT
ejpam-2347	85	36	adic	adic	ADJ
ejpam-2347	85	37	beta	beta	NOUN
ejpam-2347	85	38	function	function	NOUN
ejpam-2347	85	39	.	.	PUNCT
ejpam-2347	86	1	2	2	X
ejpam-2347	86	2	.	.	X
ejpam-2347	86	3	main	main	ADJ
ejpam-2347	86	4	results	result	NOUN
ejpam-2347	86	5	naturally	naturally	ADV
ejpam-2347	86	6	a	a	DET
ejpam-2347	86	7	p	p	ADJ
ejpam-2347	86	8	-	-	PUNCT
ejpam-2347	86	9	adic	adic	ADJ
ejpam-2347	86	10	analogue	analogue	NOUN
ejpam-2347	86	11	of	of	ADP
ejpam-2347	86	12	the	the	DET
ejpam-2347	86	13	classical	classical	ADJ
ejpam-2347	86	14	beta	beta	NOUN
ejpam-2347	86	15	function	function	NOUN
ejpam-2347	86	16	can	can	AUX
ejpam-2347	86	17	be	be	AUX
ejpam-2347	86	18	defined	define	VERB
ejpam-2347	86	19	as	as	ADP
ejpam-2347	86	20	follows	follow	VERB
ejpam-2347	86	21	.	.	PUNCT
ejpam-2347	87	1	definition	definition	NOUN
ejpam-2347	87	2	2	2	NUM
ejpam-2347	87	3	.	.	PUNCT
ejpam-2347	88	1	the	the	DET
ejpam-2347	88	2	p	p	NOUN
ejpam-2347	88	3	-	-	PUNCT
ejpam-2347	88	4	adic	adic	ADJ
ejpam-2347	88	5	beta	beta	NOUN
ejpam-2347	88	6	function	function	NOUN
ejpam-2347	88	7	bp	bp	PROPN
ejpam-2347	88	8	:	:	PUNCT
ejpam-2347	88	9	zp	zp	PROPN
ejpam-2347	88	10	×zp→	×zp→	PROPN
ejpam-2347	88	11	qp	qp	ADV
ejpam-2347	88	12	is	be	AUX
ejpam-2347	88	13	defined	define	VERB
ejpam-2347	88	14	by	by	ADP
ejpam-2347	88	15	the	the	DET
ejpam-2347	88	16	formula	formula	NOUN
ejpam-2347	88	17	bp(x	bp(x	NOUN
ejpam-2347	88	18	,	,	PUNCT
ejpam-2347	88	19	y	y	PROPN
ejpam-2347	88	20	)	)	PUNCT
ejpam-2347	88	21	:	:	PUNCT
ejpam-2347	88	22	=	=	SYM
ejpam-2347	88	23	γp	γp	PROPN
ejpam-2347	88	24	(	(	PUNCT
ejpam-2347	88	25	x)γp(y	x)γp(y	PROPN
ejpam-2347	88	26	)	)	PUNCT
ejpam-2347	88	27	γp(x	γp(x	PUNCT
ejpam-2347	89	1	+	+	CCONJ
ejpam-2347	89	2	y	y	X
ejpam-2347	89	3	)	)	PUNCT
ejpam-2347	89	4	,	,	PUNCT
ejpam-2347	89	5	x	x	X
ejpam-2347	89	6	,	,	PUNCT
ejpam-2347	89	7	y	y	PROPN
ejpam-2347	89	8	∈	∈	PROPN
ejpam-2347	89	9	zp	zp	PROPN
ejpam-2347	89	10	.	.	PUNCT
ejpam-2347	90	1	(	(	PUNCT
ejpam-2347	90	2	8)	8)	NUM
ejpam-2347	90	3	we	we	PRON
ejpam-2347	90	4	investigate	investigate	VERB
ejpam-2347	90	5	some	some	DET
ejpam-2347	90	6	properties	property	NOUN
ejpam-2347	90	7	of	of	ADP
ejpam-2347	90	8	the	the	DET
ejpam-2347	90	9	p	p	NOUN
ejpam-2347	90	10	-	-	PUNCT
ejpam-2347	90	11	adic	adic	ADJ
ejpam-2347	90	12	beta	beta	NOUN
ejpam-2347	90	13	function	function	NOUN
ejpam-2347	90	14	.	.	PUNCT
ejpam-2347	91	1	now	now	ADV
ejpam-2347	91	2	,	,	PUNCT
ejpam-2347	91	3	we	we	PRON
ejpam-2347	91	4	give	give	VERB
ejpam-2347	91	5	basic	basic	ADJ
ejpam-2347	91	6	properties	property	NOUN
ejpam-2347	91	7	of	of	ADP
ejpam-2347	91	8	the	the	DET
ejpam-2347	91	9	p	p	NOUN
ejpam-2347	91	10	-	-	PUNCT
ejpam-2347	91	11	adic	adic	ADJ
ejpam-2347	91	12	beta	beta	NOUN
ejpam-2347	91	13	function	function	NOUN
ejpam-2347	91	14	.	.	PUNCT
ejpam-2347	92	1	theorem	theorem	NOUN
ejpam-2347	92	2	1	1	NUM
ejpam-2347	92	3	.	.	PUNCT
ejpam-2347	93	1	the	the	DET
ejpam-2347	93	2	p	p	NOUN
ejpam-2347	93	3	-	-	PUNCT
ejpam-2347	93	4	adic	adic	ADJ
ejpam-2347	93	5	beta	beta	NOUN
ejpam-2347	93	6	function	function	NOUN
ejpam-2347	93	7	is	be	AUX
ejpam-2347	93	8	symmetric	symmetric	ADJ
ejpam-2347	93	9	.	.	PUNCT
ejpam-2347	94	1	namely	namely	ADV
ejpam-2347	94	2	,	,	PUNCT
ejpam-2347	94	3	bp(x	bp(x	NOUN
ejpam-2347	94	4	,	,	PUNCT
ejpam-2347	94	5	y	y	PROPN
ejpam-2347	94	6	)	)	PUNCT
ejpam-2347	94	7	=	=	PUNCT
ejpam-2347	94	8	bp(y	bp(y	X
ejpam-2347	94	9	,	,	PUNCT
ejpam-2347	94	10	x	x	NOUN
ejpam-2347	94	11	)	)	PUNCT
ejpam-2347	94	12	for	for	ADP
ejpam-2347	94	13	x	x	SYM
ejpam-2347	94	14	,	,	PUNCT
ejpam-2347	94	15	y	y	PROPN
ejpam-2347	94	16	∈	∈	PROPN
ejpam-2347	94	17	zp	zp	PROPN
ejpam-2347	94	18	.	.	PUNCT
ejpam-2347	94	19	proof	proof	NOUN
ejpam-2347	94	20	.	.	PUNCT
ejpam-2347	95	1	from	from	ADP
ejpam-2347	95	2	definition	definition	NOUN
ejpam-2347	95	3	2	2	NUM
ejpam-2347	95	4	,	,	PUNCT
ejpam-2347	95	5	we	we	PRON
ejpam-2347	95	6	can	can	AUX
ejpam-2347	95	7	prove	prove	VERB
ejpam-2347	95	8	that	that	SCONJ
ejpam-2347	95	9	the	the	DET
ejpam-2347	95	10	p	p	NOUN
ejpam-2347	95	11	-	-	PUNCT
ejpam-2347	95	12	adic	adic	ADJ
ejpam-2347	95	13	beta	beta	NOUN
ejpam-2347	95	14	function	function	NOUN
ejpam-2347	95	15	is	be	AUX
ejpam-2347	95	16	symmetric	symmetric	ADJ
ejpam-2347	95	17	:	:	PUNCT
ejpam-2347	95	18	bp(x	bp(x	NOUN
ejpam-2347	95	19	,	,	PUNCT
ejpam-2347	95	20	y	y	PROPN
ejpam-2347	95	21	)	)	PUNCT
ejpam-2347	95	22	=	=	SYM
ejpam-2347	95	23	γp	γp	PROPN
ejpam-2347	95	24	(	(	PUNCT
ejpam-2347	95	25	x)γp(y	x)γp(y	PROPN
ejpam-2347	95	26	)	)	PUNCT
ejpam-2347	95	27	γp(x	γp(x	PUNCT
ejpam-2347	96	1	+	+	CCONJ
ejpam-2347	96	2	y	y	X
ejpam-2347	96	3	)	)	PUNCT
ejpam-2347	96	4	=	=	PRON
ejpam-2347	96	5	γp	γp	PROPN
ejpam-2347	96	6	�	�	PROPN
ejpam-2347	96	7	y	y	PROPN
ejpam-2347	96	8	�	�	PROPN
ejpam-2347	96	9	γp(x	γp(x	PUNCT
ejpam-2347	96	10	)	)	PUNCT
ejpam-2347	96	11	γp(y	γp(y	PUNCT
ejpam-2347	97	1	+	+	CCONJ
ejpam-2347	97	2	x	x	X
ejpam-2347	97	3	)	)	PUNCT
ejpam-2347	97	4	=	=	NOUN
ejpam-2347	97	5	bp(y	bp(y	X
ejpam-2347	97	6	,	,	PUNCT
ejpam-2347	97	7	x	x	NOUN
ejpam-2347	97	8	)	)	PUNCT
ejpam-2347	97	9	for	for	ADP
ejpam-2347	97	10	x	x	SYM
ejpam-2347	97	11	,	,	PUNCT
ejpam-2347	97	12	y	y	PROPN
ejpam-2347	97	13	∈	∈	PROPN
ejpam-2347	97	14	zp	zp	PROPN
ejpam-2347	97	15	.	.	PUNCT
ejpam-2347	97	16	h.	h.	PROPN
ejpam-2347	97	17	menken	menken	PROPN
ejpam-2347	97	18	,	,	PUNCT
ejpam-2347	97	19	ö.	ö.	VERB
ejpam-2347	97	20	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	97	21	/	/	SYM
ejpam-2347	97	22	eur	eur	PROPN
ejpam-2347	97	23	.	.	PUNCT
ejpam-2347	98	1	j.	j.	PROPN
ejpam-2347	98	2	pure	pure	PROPN
ejpam-2347	98	3	appl	appl	PROPN
ejpam-2347	98	4	.	.	PROPN
ejpam-2347	98	5	math	math	PROPN
ejpam-2347	98	6	,	,	PUNCT
ejpam-2347	98	7	8	8	NUM
ejpam-2347	98	8	(	(	PUNCT
ejpam-2347	98	9	2015	2015	NUM
ejpam-2347	98	10	)	)	PUNCT
ejpam-2347	98	11	,	,	PUNCT
ejpam-2347	98	12	214	214	NUM
ejpam-2347	98	13	-	-	SYM
ejpam-2347	98	14	231	231	NUM
ejpam-2347	98	15	219	219	NUM
ejpam-2347	98	16	theorem	theorem	NOUN
ejpam-2347	98	17	2	2	NUM
ejpam-2347	98	18	.	.	PUNCT
ejpam-2347	99	1	for	for	ADP
ejpam-2347	99	2	x	x	PRON
ejpam-2347	99	3	,	,	PUNCT
ejpam-2347	99	4	y	y	PROPN
ejpam-2347	99	5	∈	∈	PROPN
ejpam-2347	99	6	zp	zp	PROPN
ejpam-2347	99	7	,	,	PUNCT
ejpam-2347	99	8	then	then	ADV
ejpam-2347	99	9	bp(x	bp(x	NOUN
ejpam-2347	99	10	,	,	PUNCT
ejpam-2347	99	11	y)bp(x	y)bp(x	ADJ
ejpam-2347	99	12	+	+	NOUN
ejpam-2347	99	13	y	y	NOUN
ejpam-2347	99	14	,	,	PUNCT
ejpam-2347	99	15	1−	1−	NUM
ejpam-2347	99	16	y	y	NOUN
ejpam-2347	99	17	)	)	PUNCT
ejpam-2347	99	18	=	=	PUNCT
ejpam-2347	100	1			PROPN
ejpam-2347	100	2			PROPN
ejpam-2347	100	3			PROPN
ejpam-2347	100	4	(	(	PUNCT
ejpam-2347	100	5	−1)ℓ(y	−1)ℓ(y	PROPN
ejpam-2347	100	6	)	)	PUNCT
ejpam-2347	100	7	hp(x	hp(x	PROPN
ejpam-2347	100	8	)	)	PUNCT
ejpam-2347	100	9	,	,	PUNCT
ejpam-2347	100	10	p	p	X
ejpam-2347	100	11	6=	6=	ADP
ejpam-2347	100	12	2	2	NUM
ejpam-2347	100	13	(	(	PUNCT
ejpam-2347	100	14	−1)σ1(y)+1	−1)σ1(y)+1	PROPN
ejpam-2347	100	15	hp(x	hp(x	NOUN
ejpam-2347	100	16	)	)	PUNCT
ejpam-2347	100	17	p	p	X
ejpam-2347	101	1	=	=	NOUN
ejpam-2347	101	2	2	2	NUM
ejpam-2347	101	3	where	where	SCONJ
ejpam-2347	101	4	hp(x	hp(x	ADV
ejpam-2347	101	5	)	)	PUNCT
ejpam-2347	101	6	:	:	PUNCT
ejpam-2347	101	7	=	=	SYM
ejpam-2347	101	8	¨	¨	NOUN
ejpam-2347	101	9	−x	−x	NOUN
ejpam-2347	101	10	if	if	SCONJ
ejpam-2347	101	11	|x	|x	NOUN
ejpam-2347	101	12	|p	|p	X
ejpam-2347	101	13	=	=	SYM
ejpam-2347	101	14	1	1	NUM
ejpam-2347	101	15	−1	−1	NOUN
ejpam-2347	101	16	if	if	SCONJ
ejpam-2347	101	17	|x	|x	PRON
ejpam-2347	101	18	|p	|p	VERB
ejpam-2347	101	19	<	<	X
ejpam-2347	101	20	1	1	NUM
ejpam-2347	101	21	and	and	CCONJ
ejpam-2347	101	22	ℓ	ℓ	PROPN
ejpam-2347	101	23	:	:	PUNCT
ejpam-2347	102	1	zp	zp	PROPN
ejpam-2347	102	2	→	→	SYM
ejpam-2347	102	3	�	�	PROPN
ejpam-2347	102	4	1,2	1,2	NUM
ejpam-2347	102	5	,	,	PUNCT
ejpam-2347	102	6	.	.	PUNCT
ejpam-2347	102	7	.	.	PUNCT
ejpam-2347	102	8	.	.	PUNCT
ejpam-2347	103	1	,	,	PUNCT
ejpam-2347	103	2	p	p	NOUN
ejpam-2347	103	3	assigns	assign	VERB
ejpam-2347	103	4	to	to	ADP
ejpam-2347	103	5	x	x	PUNCT
ejpam-2347	103	6	∈	∈	PROPN
ejpam-2347	103	7	zp	zp	NOUN
ejpam-2347	103	8	its	its	PRON
ejpam-2347	103	9	residue	residue	NOUN
ejpam-2347	103	10	∈	∈	PROPN
ejpam-2347	103	11	�	�	NOUN
ejpam-2347	103	12	1,2	1,2	NUM
ejpam-2347	103	13	,	,	PUNCT
ejpam-2347	103	14	.	.	PUNCT
ejpam-2347	103	15	.	.	PUNCT
ejpam-2347	104	1	.	.	PUNCT
ejpam-2347	105	1	,	,	PUNCT
ejpam-2347	105	2	p	p	X
ejpam-2347	105	3	modulo	modulo	ADJ
ejpam-2347	105	4	pzp	pzp	NOUN
ejpam-2347	105	5	and	and	CCONJ
ejpam-2347	105	6	σ1	σ1	PROPN
ejpam-2347	105	7	is	be	AUX
ejpam-2347	105	8	defined	define	VERB
ejpam-2347	105	9	by	by	ADP
ejpam-2347	105	10	the	the	DET
ejpam-2347	105	11	formula	formula	NOUN
ejpam-2347	105	12	σ1	σ1	PROPN
ejpam-2347	105	13	(	(	PUNCT
ejpam-2347	105	14	∞	∞	PROPN
ejpam-2347	105	15	∑	∑	PUNCT
ejpam-2347	105	16	j=0	j=0	PROPN
ejpam-2347	105	17	a	a	DET
ejpam-2347	105	18	j2	j2	PROPN
ejpam-2347	105	19	j	j	PROPN
ejpam-2347	105	20	)	)	PUNCT
ejpam-2347	105	21	=	=	NOUN
ejpam-2347	105	22	a1	a1	NOUN
ejpam-2347	105	23	proof	proof	NOUN
ejpam-2347	105	24	.	.	PUNCT
ejpam-2347	106	1	let	let	VERB
ejpam-2347	106	2	p	p	PRON
ejpam-2347	106	3	6=	6=	ADP
ejpam-2347	106	4	2	2	NUM
ejpam-2347	106	5	.	.	PUNCT
ejpam-2347	106	6	from	from	ADP
ejpam-2347	106	7	definition	definition	NOUN
ejpam-2347	106	8	2	2	NUM
ejpam-2347	106	9	and	and	CCONJ
ejpam-2347	106	10	proposition	proposition	NOUN
ejpam-2347	106	11	1	1	NUM
ejpam-2347	106	12	it	it	PRON
ejpam-2347	106	13	follows	follow	VERB
ejpam-2347	106	14	that	that	SCONJ
ejpam-2347	106	15	bp(x	bp(x	NOUN
ejpam-2347	106	16	,	,	PUNCT
ejpam-2347	106	17	y)bp(x	y)bp(x	SYM
ejpam-2347	106	18	+	+	NOUN
ejpam-2347	106	19	y	y	NOUN
ejpam-2347	106	20	,	,	PUNCT
ejpam-2347	106	21	1−	1−	NUM
ejpam-2347	106	22	y	y	NOUN
ejpam-2347	106	23	)	)	PUNCT
ejpam-2347	106	24	=	=	PRON
ejpam-2347	106	25	γp	γp	PROPN
ejpam-2347	106	26	(	(	PUNCT
ejpam-2347	106	27	x)γp(y	x)γp(y	PROPN
ejpam-2347	106	28	)	)	PUNCT
ejpam-2347	106	29	γp(x	γp(x	PUNCT
ejpam-2347	107	1	+	+	CCONJ
ejpam-2347	107	2	y	y	X
ejpam-2347	107	3	)	)	PUNCT
ejpam-2347	107	4	γp	γp	PROPN
ejpam-2347	107	5	�	�	PROPN
ejpam-2347	107	6	x	x	PUNCT
ejpam-2347	108	1	+	+	CCONJ
ejpam-2347	108	2	y	y	PROPN
ejpam-2347	108	3	�	�	PROPN
ejpam-2347	108	4	γp(1−	γp(1−	PROPN
ejpam-2347	108	5	y	y	NOUN
ejpam-2347	108	6	)	)	PUNCT
ejpam-2347	108	7	γp(x	γp(x	PUNCT
ejpam-2347	108	8	+	+	NOUN
ejpam-2347	108	9	1	1	X
ejpam-2347	108	10	)	)	PUNCT
ejpam-2347	108	11	=	=	PRON
ejpam-2347	108	12	γp	γp	PROPN
ejpam-2347	108	13	(	(	PUNCT
ejpam-2347	108	14	x)γp(y)γp(1−	x)γp(y)γp(1−	NOUN
ejpam-2347	108	15	y	y	PROPN
ejpam-2347	108	16	)	)	PUNCT
ejpam-2347	108	17	γp(x	γp(x	PUNCT
ejpam-2347	108	18	+	+	NOUN
ejpam-2347	108	19	1	1	X
ejpam-2347	108	20	)	)	PUNCT
ejpam-2347	108	21	=	=	PRON
ejpam-2347	108	22	γp	γp	PROPN
ejpam-2347	108	23	(	(	PUNCT
ejpam-2347	108	24	x)γp(y)γp(1−	x)γp(y)γp(1−	NOUN
ejpam-2347	108	25	y	y	X
ejpam-2347	108	26	)	)	PUNCT
ejpam-2347	108	27	γp(x)hp(x	γp(x)hp(x	PROPN
ejpam-2347	108	28	)	)	PUNCT
ejpam-2347	108	29	=	=	SYM
ejpam-2347	108	30	γp(y)γp(1−	γp(y)γp(1−	PROPN
ejpam-2347	108	31	y	y	PROPN
ejpam-2347	108	32	)	)	PUNCT
ejpam-2347	108	33	hp(x	hp(x	PROPN
ejpam-2347	108	34	)	)	PUNCT
ejpam-2347	108	35	,	,	PUNCT
ejpam-2347	108	36	and	and	CCONJ
ejpam-2347	108	37	by	by	ADP
ejpam-2347	108	38	proposition	proposition	NOUN
ejpam-2347	108	39	3	3	NUM
ejpam-2347	108	40	we	we	PRON
ejpam-2347	108	41	obtain	obtain	VERB
ejpam-2347	108	42	that	that	DET
ejpam-2347	108	43	bp(x	bp(x	NOUN
ejpam-2347	108	44	,	,	PUNCT
ejpam-2347	108	45	y)bp(x	y)bp(x	SYM
ejpam-2347	108	46	+	+	NOUN
ejpam-2347	108	47	y	y	NOUN
ejpam-2347	108	48	,	,	PUNCT
ejpam-2347	108	49	1−	1−	NUM
ejpam-2347	108	50	y	y	NOUN
ejpam-2347	108	51	)	)	PUNCT
ejpam-2347	108	52	=	=	PRON
ejpam-2347	108	53	(	(	PUNCT
ejpam-2347	108	54	−1)ℓ(y	−1)ℓ(y	PROPN
ejpam-2347	108	55	)	)	PUNCT
ejpam-2347	108	56	hp(x	hp(x	PROPN
ejpam-2347	108	57	)	)	PUNCT
ejpam-2347	108	58	.	.	PUNCT
ejpam-2347	109	1	in	in	ADP
ejpam-2347	109	2	similar	similar	ADJ
ejpam-2347	109	3	way	way	NOUN
ejpam-2347	109	4	,	,	PUNCT
ejpam-2347	109	5	we	we	PRON
ejpam-2347	109	6	can	can	AUX
ejpam-2347	109	7	prove	prove	VERB
ejpam-2347	109	8	the	the	DET
ejpam-2347	109	9	theorem	theorem	NOUN
ejpam-2347	109	10	for	for	ADP
ejpam-2347	109	11	p	p	NOUN
ejpam-2347	109	12	=	=	SYM
ejpam-2347	109	13	2	2	NUM
ejpam-2347	109	14	.	.	PUNCT
ejpam-2347	109	15	theorem	theorem	NOUN
ejpam-2347	109	16	3	3	NUM
ejpam-2347	109	17	.	.	PUNCT
ejpam-2347	109	18	the	the	DET
ejpam-2347	109	19	equality	equality	NOUN
ejpam-2347	109	20	bp(x	bp(x	PUNCT
ejpam-2347	109	21	+	+	NOUN
ejpam-2347	109	22	1	1	NUM
ejpam-2347	109	23	,	,	PUNCT
ejpam-2347	109	24	y	y	NOUN
ejpam-2347	109	25	)	)	PUNCT
ejpam-2347	109	26	=	=	SYM
ejpam-2347	109	27	hp(x	hp(x	PROPN
ejpam-2347	109	28	)	)	PUNCT
ejpam-2347	109	29	hp(x	hp(x	PROPN
ejpam-2347	109	30	+	+	PROPN
ejpam-2347	109	31	y	y	NOUN
ejpam-2347	109	32	)	)	PUNCT
ejpam-2347	109	33	bp(x	bp(x	NOUN
ejpam-2347	109	34	,	,	PUNCT
ejpam-2347	109	35	y	y	X
ejpam-2347	109	36	)	)	PUNCT
ejpam-2347	109	37	holds	hold	VERB
ejpam-2347	109	38	for	for	ADP
ejpam-2347	109	39	all	all	PRON
ejpam-2347	109	40	x	x	SYM
ejpam-2347	109	41	,	,	PUNCT
ejpam-2347	109	42	y	y	PROPN
ejpam-2347	109	43	∈	∈	PROPN
ejpam-2347	109	44	zp	zp	PROPN
ejpam-2347	109	45	.	.	PUNCT
ejpam-2347	109	46	proof	proof	NOUN
ejpam-2347	109	47	.	.	PUNCT
ejpam-2347	110	1	by	by	ADP
ejpam-2347	110	2	using	use	VERB
ejpam-2347	110	3	definition	definition	NOUN
ejpam-2347	110	4	2	2	NUM
ejpam-2347	110	5	and	and	CCONJ
ejpam-2347	110	6	proposition	proposition	NOUN
ejpam-2347	110	7	1	1	NUM
ejpam-2347	110	8	we	we	PRON
ejpam-2347	110	9	have	have	VERB
ejpam-2347	110	10	that	that	PRON
ejpam-2347	110	11	bp(x	bp(x	PUNCT
ejpam-2347	110	12	+	+	NOUN
ejpam-2347	110	13	1	1	NUM
ejpam-2347	110	14	,	,	PUNCT
ejpam-2347	110	15	y	y	NOUN
ejpam-2347	110	16	)	)	PUNCT
ejpam-2347	110	17	=	=	SYM
ejpam-2347	110	18	γp	γp	PROPN
ejpam-2347	110	19	(	(	PUNCT
ejpam-2347	110	20	x	x	PROPN
ejpam-2347	110	21	+	+	NUM
ejpam-2347	110	22	1)γp(y	1)γp(y	NUM
ejpam-2347	110	23	)	)	PUNCT
ejpam-2347	110	24	γp(x	γp(x	PUNCT
ejpam-2347	111	1	+	+	PUNCT
ejpam-2347	111	2	1	1	NUM
ejpam-2347	111	3	+	+	NUM
ejpam-2347	111	4	y	y	NOUN
ejpam-2347	111	5	)	)	PUNCT
ejpam-2347	111	6	h.	h.	PROPN
ejpam-2347	111	7	menken	menken	PROPN
ejpam-2347	111	8	,	,	PUNCT
ejpam-2347	111	9	ö.	ö.	VERB
ejpam-2347	111	10	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	111	11	/	/	SYM
ejpam-2347	111	12	eur	eur	PROPN
ejpam-2347	111	13	.	.	PUNCT
ejpam-2347	112	1	j.	j.	PROPN
ejpam-2347	112	2	pure	pure	PROPN
ejpam-2347	112	3	appl	appl	PROPN
ejpam-2347	112	4	.	.	PROPN
ejpam-2347	112	5	math	math	PROPN
ejpam-2347	112	6	,	,	PUNCT
ejpam-2347	112	7	8	8	NUM
ejpam-2347	112	8	(	(	PUNCT
ejpam-2347	112	9	2015	2015	NUM
ejpam-2347	112	10	)	)	PUNCT
ejpam-2347	112	11	,	,	PUNCT
ejpam-2347	112	12	214	214	NUM
ejpam-2347	112	13	-	-	SYM
ejpam-2347	112	14	231	231	NUM
ejpam-2347	112	15	220	220	NUM
ejpam-2347	112	16	=	=	SYM
ejpam-2347	112	17	γp	γp	X
ejpam-2347	112	18	(	(	PUNCT
ejpam-2347	112	19	x)hp(x)γp(y	x)hp(x)γp(y	PROPN
ejpam-2347	112	20	)	)	PUNCT
ejpam-2347	112	21	γp((x	γp((x	NOUN
ejpam-2347	113	1	+	+	CCONJ
ejpam-2347	113	2	y	y	NOUN
ejpam-2347	113	3	)	)	PUNCT
ejpam-2347	114	1	+	+	NOUN
ejpam-2347	114	2	1	1	X
ejpam-2347	114	3	)	)	PUNCT
ejpam-2347	114	4	=	=	PRON
ejpam-2347	114	5	γp	γp	PROPN
ejpam-2347	114	6	(	(	PUNCT
ejpam-2347	114	7	x)hp(x)γp(y	x)hp(x)γp(y	PROPN
ejpam-2347	114	8	)	)	PUNCT
ejpam-2347	114	9	γp(x	γp(x	PUNCT
ejpam-2347	115	1	+	+	CCONJ
ejpam-2347	115	2	y)hp(x	y)hp(x	PROPN
ejpam-2347	115	3	+	+	NOUN
ejpam-2347	115	4	y	y	NOUN
ejpam-2347	115	5	)	)	PUNCT
ejpam-2347	115	6	=	=	SYM
ejpam-2347	115	7	hp(x	hp(x	PROPN
ejpam-2347	115	8	)	)	PUNCT
ejpam-2347	115	9	hp(x	hp(x	PROPN
ejpam-2347	115	10	+	+	PROPN
ejpam-2347	115	11	y	y	PROPN
ejpam-2347	115	12	)	)	PUNCT
ejpam-2347	115	13	γp	γp	PROPN
ejpam-2347	115	14	(	(	PUNCT
ejpam-2347	115	15	x)γp(y	x)γp(y	PROPN
ejpam-2347	115	16	)	)	PUNCT
ejpam-2347	115	17	γp(x	γp(x	PUNCT
ejpam-2347	116	1	+	+	CCONJ
ejpam-2347	116	2	y	y	X
ejpam-2347	116	3	)	)	PUNCT
ejpam-2347	116	4	=	=	SYM
ejpam-2347	117	1	hp(x	hp(x	PROPN
ejpam-2347	117	2	)	)	PUNCT
ejpam-2347	118	1	hp(x	hp(x	PROPN
ejpam-2347	118	2	+	+	PROPN
ejpam-2347	118	3	y	y	NOUN
ejpam-2347	118	4	)	)	PUNCT
ejpam-2347	118	5	bp(x	bp(x	NOUN
ejpam-2347	118	6	,	,	PUNCT
ejpam-2347	118	7	y	y	PROPN
ejpam-2347	118	8	)	)	PUNCT
ejpam-2347	118	9	.	.	PUNCT
ejpam-2347	119	1	theorem	theorem	ADJ
ejpam-2347	119	2	4	4	NUM
ejpam-2347	119	3	.	.	PUNCT
ejpam-2347	120	1	the	the	DET
ejpam-2347	120	2	equality	equality	NOUN
ejpam-2347	120	3	bp(x	bp(x	PUNCT
ejpam-2347	120	4	,	,	PUNCT
ejpam-2347	120	5	y	y	PROPN
ejpam-2347	120	6	+	+	NOUN
ejpam-2347	120	7	1	1	X
ejpam-2347	120	8	)	)	PUNCT
ejpam-2347	120	9	=	=	NOUN
ejpam-2347	120	10	hp(y	hp(y	X
ejpam-2347	120	11	)	)	PUNCT
ejpam-2347	120	12	hp(x	hp(x	PROPN
ejpam-2347	120	13	+	+	PROPN
ejpam-2347	120	14	y	y	NOUN
ejpam-2347	120	15	)	)	PUNCT
ejpam-2347	120	16	bp(x	bp(x	NOUN
ejpam-2347	120	17	,	,	PUNCT
ejpam-2347	120	18	y	y	X
ejpam-2347	120	19	)	)	PUNCT
ejpam-2347	120	20	holds	hold	VERB
ejpam-2347	120	21	for	for	ADP
ejpam-2347	120	22	all	all	PRON
ejpam-2347	120	23	x	x	SYM
ejpam-2347	120	24	,	,	PUNCT
ejpam-2347	120	25	y	y	PROPN
ejpam-2347	120	26	∈	∈	PROPN
ejpam-2347	120	27	zp	zp	PROPN
ejpam-2347	120	28	.	.	PUNCT
ejpam-2347	120	29	proof	proof	NOUN
ejpam-2347	120	30	.	.	PUNCT
ejpam-2347	121	1	from	from	ADP
ejpam-2347	121	2	definition	definition	NOUN
ejpam-2347	121	3	2	2	NUM
ejpam-2347	121	4	and	and	CCONJ
ejpam-2347	121	5	proposition	proposition	NOUN
ejpam-2347	121	6	1	1	NUM
ejpam-2347	121	7	we	we	PRON
ejpam-2347	121	8	get	get	VERB
ejpam-2347	121	9	bp(x	bp(x	PUNCT
ejpam-2347	121	10	,	,	PUNCT
ejpam-2347	121	11	y	y	PROPN
ejpam-2347	122	1	+	+	NOUN
ejpam-2347	122	2	1	1	X
ejpam-2347	122	3	)	)	PUNCT
ejpam-2347	122	4	=	=	PRON
ejpam-2347	122	5	γp	γp	PROPN
ejpam-2347	122	6	(	(	PUNCT
ejpam-2347	122	7	x)γp(y	x)γp(y	PROPN
ejpam-2347	122	8	+	+	PROPN
ejpam-2347	122	9	1	1	NUM
ejpam-2347	122	10	)	)	PUNCT
ejpam-2347	122	11	γp(x	γp(x	PUNCT
ejpam-2347	123	1	+	+	CCONJ
ejpam-2347	123	2	y	y	PROPN
ejpam-2347	124	1	+	+	CCONJ
ejpam-2347	124	2	1	1	X
ejpam-2347	124	3	)	)	PUNCT
ejpam-2347	124	4	=	=	PRON
ejpam-2347	124	5	γp	γp	PROPN
ejpam-2347	124	6	(	(	PUNCT
ejpam-2347	124	7	x)hp(y)γp(y	x)hp(y)γp(y	PROPN
ejpam-2347	124	8	)	)	PUNCT
ejpam-2347	124	9	γp((x	γp((x	NOUN
ejpam-2347	125	1	+	+	CCONJ
ejpam-2347	125	2	y	y	NOUN
ejpam-2347	125	3	)	)	PUNCT
ejpam-2347	126	1	+	+	NOUN
ejpam-2347	126	2	1	1	X
ejpam-2347	126	3	)	)	PUNCT
ejpam-2347	126	4	=	=	PRON
ejpam-2347	126	5	γp	γp	PROPN
ejpam-2347	126	6	(	(	PUNCT
ejpam-2347	126	7	x)hp(y)γp(y	x)hp(y)γp(y	NUM
ejpam-2347	126	8	)	)	PUNCT
ejpam-2347	126	9	γp(x	γp(x	PUNCT
ejpam-2347	127	1	+	+	CCONJ
ejpam-2347	127	2	y)hp(x	y)hp(x	PROPN
ejpam-2347	127	3	+	+	NOUN
ejpam-2347	127	4	y	y	NOUN
ejpam-2347	127	5	)	)	PUNCT
ejpam-2347	127	6	=	=	PUNCT
ejpam-2347	127	7	hp(y	hp(y	X
ejpam-2347	127	8	)	)	PUNCT
ejpam-2347	127	9	hp(x	hp(x	PROPN
ejpam-2347	127	10	+	+	PROPN
ejpam-2347	127	11	y	y	PROPN
ejpam-2347	127	12	)	)	PUNCT
ejpam-2347	127	13	γp	γp	PROPN
ejpam-2347	127	14	(	(	PUNCT
ejpam-2347	127	15	x)γp(y	x)γp(y	PROPN
ejpam-2347	127	16	)	)	PUNCT
ejpam-2347	127	17	γp(x	γp(x	PUNCT
ejpam-2347	128	1	+	+	CCONJ
ejpam-2347	128	2	y	y	X
ejpam-2347	128	3	)	)	PUNCT
ejpam-2347	128	4	=	=	PUNCT
ejpam-2347	129	1	hp(y	hp(y	X
ejpam-2347	129	2	)	)	PUNCT
ejpam-2347	130	1	hp(x	hp(x	PROPN
ejpam-2347	130	2	+	+	PROPN
ejpam-2347	130	3	y	y	NOUN
ejpam-2347	130	4	)	)	PUNCT
ejpam-2347	130	5	bp(x	bp(x	NOUN
ejpam-2347	130	6	,	,	PUNCT
ejpam-2347	130	7	y	y	PROPN
ejpam-2347	130	8	)	)	PUNCT
ejpam-2347	130	9	.	.	PUNCT
ejpam-2347	131	1	corollary	corollary	ADJ
ejpam-2347	131	2	3	3	NUM
ejpam-2347	131	3	.	.	PUNCT
ejpam-2347	132	1	the	the	DET
ejpam-2347	132	2	relation	relation	NOUN
ejpam-2347	132	3	bp(x	bp(x	PUNCT
ejpam-2347	132	4	+	+	NOUN
ejpam-2347	132	5	1	1	NUM
ejpam-2347	132	6	,	,	PUNCT
ejpam-2347	132	7	y	y	PROPN
ejpam-2347	132	8	)	)	PUNCT
ejpam-2347	132	9	+	+	CCONJ
ejpam-2347	132	10	bp(x	bp(x	X
ejpam-2347	132	11	,	,	PUNCT
ejpam-2347	132	12	y	y	PROPN
ejpam-2347	132	13	+	+	NOUN
ejpam-2347	132	14	1	1	X
ejpam-2347	132	15	)	)	PUNCT
ejpam-2347	132	16	=	=	SYM
ejpam-2347	132	17	hp(x	hp(x	PROPN
ejpam-2347	132	18	)	)	PUNCT
ejpam-2347	132	19	+	+	NUM
ejpam-2347	132	20	hp(y	hp(y	NOUN
ejpam-2347	132	21	)	)	PUNCT
ejpam-2347	132	22	hp(x	hp(x	PROPN
ejpam-2347	132	23	+	+	PROPN
ejpam-2347	132	24	y	y	NOUN
ejpam-2347	132	25	)	)	PUNCT
ejpam-2347	132	26	bp(x	bp(x	NOUN
ejpam-2347	132	27	,	,	PUNCT
ejpam-2347	132	28	y	y	X
ejpam-2347	132	29	)	)	PUNCT
ejpam-2347	132	30	holds	hold	VERB
ejpam-2347	132	31	for	for	ADP
ejpam-2347	132	32	all	all	PRON
ejpam-2347	132	33	x	x	SYM
ejpam-2347	132	34	,	,	PUNCT
ejpam-2347	132	35	y	y	PROPN
ejpam-2347	132	36	∈	∈	PROPN
ejpam-2347	132	37	zp	zp	PROPN
ejpam-2347	132	38	.	.	PUNCT
ejpam-2347	132	39	proof	proof	NOUN
ejpam-2347	132	40	.	.	PUNCT
ejpam-2347	133	1	according	accord	VERB
ejpam-2347	133	2	to	to	ADP
ejpam-2347	133	3	theorem	theorem	ADJ
ejpam-2347	133	4	3	3	NUM
ejpam-2347	133	5	and	and	CCONJ
ejpam-2347	133	6	theorem	theorem	VERB
ejpam-2347	133	7	4	4	NUM
ejpam-2347	133	8	we	we	PRON
ejpam-2347	133	9	have	have	VERB
ejpam-2347	133	10	bp(x	bp(x	NOUN
ejpam-2347	133	11	+	+	NOUN
ejpam-2347	133	12	1	1	NUM
ejpam-2347	133	13	,	,	PUNCT
ejpam-2347	133	14	y	y	PROPN
ejpam-2347	133	15	)	)	PUNCT
ejpam-2347	133	16	+	+	CCONJ
ejpam-2347	133	17	bp(x	bp(x	X
ejpam-2347	133	18	,	,	PUNCT
ejpam-2347	133	19	y	y	PROPN
ejpam-2347	133	20	+	+	NOUN
ejpam-2347	133	21	1	1	X
ejpam-2347	133	22	)	)	PUNCT
ejpam-2347	133	23	=	=	SYM
ejpam-2347	133	24	hp(x	hp(x	PROPN
ejpam-2347	133	25	)	)	PUNCT
ejpam-2347	133	26	hp(x	hp(x	PROPN
ejpam-2347	133	27	+	+	PROPN
ejpam-2347	133	28	y	y	NOUN
ejpam-2347	133	29	)	)	PUNCT
ejpam-2347	133	30	bp(x	bp(x	NOUN
ejpam-2347	133	31	,	,	PUNCT
ejpam-2347	133	32	y	y	PROPN
ejpam-2347	133	33	)	)	PUNCT
ejpam-2347	133	34	+	+	NUM
ejpam-2347	133	35	hp(y	hp(y	NOUN
ejpam-2347	133	36	)	)	PUNCT
ejpam-2347	133	37	hp(x	hp(x	PROPN
ejpam-2347	133	38	+	+	PROPN
ejpam-2347	133	39	y	y	NOUN
ejpam-2347	133	40	)	)	PUNCT
ejpam-2347	133	41	bp(x	bp(x	NOUN
ejpam-2347	133	42	,	,	PUNCT
ejpam-2347	133	43	y	y	PROPN
ejpam-2347	133	44	)	)	PUNCT
ejpam-2347	133	45	h.	h.	PROPN
ejpam-2347	133	46	menken	menken	PROPN
ejpam-2347	133	47	,	,	PUNCT
ejpam-2347	133	48	ö.	ö.	VERB
ejpam-2347	133	49	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	133	50	/	/	SYM
ejpam-2347	133	51	eur	eur	PROPN
ejpam-2347	133	52	.	.	PUNCT
ejpam-2347	134	1	j.	j.	PROPN
ejpam-2347	134	2	pure	pure	PROPN
ejpam-2347	134	3	appl	appl	PROPN
ejpam-2347	134	4	.	.	PROPN
ejpam-2347	134	5	math	math	PROPN
ejpam-2347	134	6	,	,	PUNCT
ejpam-2347	134	7	8	8	NUM
ejpam-2347	134	8	(	(	PUNCT
ejpam-2347	134	9	2015	2015	NUM
ejpam-2347	134	10	)	)	PUNCT
ejpam-2347	134	11	,	,	PUNCT
ejpam-2347	134	12	214	214	NUM
ejpam-2347	134	13	-	-	SYM
ejpam-2347	134	14	231	231	NUM
ejpam-2347	134	15	221	221	NUM
ejpam-2347	134	16	=	=	SYM
ejpam-2347	134	17	hp(x	hp(x	PROPN
ejpam-2347	134	18	)	)	PUNCT
ejpam-2347	134	19	+	+	NUM
ejpam-2347	134	20	hp(y	hp(y	NOUN
ejpam-2347	134	21	)	)	PUNCT
ejpam-2347	134	22	hp(x	hp(x	PROPN
ejpam-2347	134	23	+	+	PROPN
ejpam-2347	134	24	y	y	NOUN
ejpam-2347	134	25	)	)	PUNCT
ejpam-2347	134	26	bp(x	bp(x	NOUN
ejpam-2347	134	27	,	,	PUNCT
ejpam-2347	134	28	y	y	PROPN
ejpam-2347	134	29	)	)	PUNCT
ejpam-2347	134	30	.	.	PUNCT
ejpam-2347	135	1	corollary	corollary	ADJ
ejpam-2347	135	2	4	4	NUM
ejpam-2347	135	3	.	.	PUNCT
ejpam-2347	136	1	for	for	ADP
ejpam-2347	136	2	all	all	DET
ejpam-2347	136	3	x	x	SYM
ejpam-2347	136	4	,	,	PUNCT
ejpam-2347	136	5	y	y	PROPN
ejpam-2347	136	6	∈	∈	PROPN
ejpam-2347	136	7	zp	zp	PROPN
ejpam-2347	136	8	,	,	PUNCT
ejpam-2347	136	9	the	the	DET
ejpam-2347	136	10	equality	equality	NOUN
ejpam-2347	136	11	bp(x	bp(x	PUNCT
ejpam-2347	136	12	,	,	PUNCT
ejpam-2347	136	13	y	y	PROPN
ejpam-2347	136	14	+	+	NOUN
ejpam-2347	136	15	1	1	X
ejpam-2347	136	16	)	)	PUNCT
ejpam-2347	136	17	=	=	NOUN
ejpam-2347	136	18	hp(y	hp(y	X
ejpam-2347	136	19	)	)	PUNCT
ejpam-2347	136	20	hp(x	hp(x	NOUN
ejpam-2347	136	21	)	)	PUNCT
ejpam-2347	136	22	bp(x	bp(x	NOUN
ejpam-2347	136	23	+	+	NOUN
ejpam-2347	136	24	1	1	NUM
ejpam-2347	136	25	,	,	PUNCT
ejpam-2347	136	26	y	y	NOUN
ejpam-2347	136	27	)	)	PUNCT
ejpam-2347	136	28	holds	hold	VERB
ejpam-2347	136	29	.	.	PUNCT
ejpam-2347	137	1	proof	proof	NOUN
ejpam-2347	137	2	.	.	PUNCT
ejpam-2347	138	1	it	it	PRON
ejpam-2347	138	2	follows	follow	VERB
ejpam-2347	138	3	from	from	ADP
ejpam-2347	138	4	theorem	theorem	ADJ
ejpam-2347	138	5	3	3	NUM
ejpam-2347	138	6	that	that	DET
ejpam-2347	138	7	bp(x	bp(x	NOUN
ejpam-2347	138	8	,	,	PUNCT
ejpam-2347	138	9	y	y	PROPN
ejpam-2347	138	10	)	)	PUNCT
ejpam-2347	138	11	=	=	SYM
ejpam-2347	138	12	hp(x	hp(x	PROPN
ejpam-2347	138	13	+	+	PROPN
ejpam-2347	138	14	y	y	NOUN
ejpam-2347	138	15	)	)	PUNCT
ejpam-2347	138	16	hp(x	hp(x	PROPN
ejpam-2347	138	17	)	)	PUNCT
ejpam-2347	138	18	bp(x	bp(x	NOUN
ejpam-2347	139	1	+	+	NOUN
ejpam-2347	139	2	1	1	NUM
ejpam-2347	139	3	,	,	PUNCT
ejpam-2347	139	4	y	y	NOUN
ejpam-2347	139	5	)	)	PUNCT
ejpam-2347	139	6	.	.	PUNCT
ejpam-2347	140	1	(	(	PUNCT
ejpam-2347	140	2	9	9	X
ejpam-2347	140	3	)	)	PUNCT
ejpam-2347	140	4	using	use	VERB
ejpam-2347	140	5	(	(	PUNCT
ejpam-2347	140	6	9	9	NUM
ejpam-2347	140	7	)	)	PUNCT
ejpam-2347	140	8	in	in	ADP
ejpam-2347	140	9	theorem	theorem	NOUN
ejpam-2347	140	10	4	4	NUM
ejpam-2347	140	11	we	we	PRON
ejpam-2347	140	12	obtain	obtain	VERB
ejpam-2347	140	13	that	that	DET
ejpam-2347	140	14	bp(x	bp(x	NOUN
ejpam-2347	140	15	,	,	PUNCT
ejpam-2347	140	16	y	y	PROPN
ejpam-2347	140	17	+	+	NOUN
ejpam-2347	140	18	1	1	X
ejpam-2347	140	19	)	)	PUNCT
ejpam-2347	140	20	=	=	NOUN
ejpam-2347	140	21	hp(y	hp(y	X
ejpam-2347	140	22	)	)	PUNCT
ejpam-2347	140	23	hp(x	hp(x	PROPN
ejpam-2347	140	24	+	+	PROPN
ejpam-2347	140	25	y	y	NOUN
ejpam-2347	140	26	)	)	PUNCT
ejpam-2347	140	27	hp(x	hp(x	PROPN
ejpam-2347	141	1	+	+	PROPN
ejpam-2347	141	2	y	y	NOUN
ejpam-2347	141	3	)	)	PUNCT
ejpam-2347	141	4	hp(x	hp(x	PROPN
ejpam-2347	141	5	)	)	PUNCT
ejpam-2347	142	1	bp(x	bp(x	NOUN
ejpam-2347	143	1	+	+	NOUN
ejpam-2347	143	2	1	1	NUM
ejpam-2347	143	3	,	,	PUNCT
ejpam-2347	143	4	y	y	NOUN
ejpam-2347	143	5	)	)	PUNCT
ejpam-2347	143	6	=	=	PUNCT
ejpam-2347	144	1	hp(y	hp(y	X
ejpam-2347	144	2	)	)	PUNCT
ejpam-2347	144	3	hp(x	hp(x	NOUN
ejpam-2347	144	4	)	)	PUNCT
ejpam-2347	144	5	bp(x	bp(x	NOUN
ejpam-2347	145	1	+	+	NOUN
ejpam-2347	145	2	1	1	NUM
ejpam-2347	145	3	,	,	PUNCT
ejpam-2347	145	4	y	y	NOUN
ejpam-2347	145	5	)	)	PUNCT
ejpam-2347	145	6	.	.	PUNCT
ejpam-2347	146	1	theorem	theorem	NOUN
ejpam-2347	146	2	5	5	NUM
ejpam-2347	146	3	.	.	PUNCT
ejpam-2347	147	1	the	the	DET
ejpam-2347	147	2	equality	equality	NOUN
ejpam-2347	147	3	bp(x	bp(x	PUNCT
ejpam-2347	147	4	+	+	NOUN
ejpam-2347	147	5	1	1	NUM
ejpam-2347	147	6	,	,	PUNCT
ejpam-2347	147	7	y	y	PROPN
ejpam-2347	147	8	+	+	NOUN
ejpam-2347	147	9	1	1	X
ejpam-2347	147	10	)	)	PUNCT
ejpam-2347	147	11	=	=	SYM
ejpam-2347	147	12	hp(x)hp(y	hp(x)hp(y	X
ejpam-2347	147	13	)	)	PUNCT
ejpam-2347	147	14	hp(x	hp(x	PROPN
ejpam-2347	148	1	+	+	NOUN
ejpam-2347	148	2	y	y	PROPN
ejpam-2347	148	3	+	+	CCONJ
ejpam-2347	148	4	1)hp(x	1)hp(x	NUM
ejpam-2347	149	1	+	+	CCONJ
ejpam-2347	149	2	y	y	NOUN
ejpam-2347	149	3	)	)	PUNCT
ejpam-2347	149	4	bp(x	bp(x	NOUN
ejpam-2347	149	5	,	,	PUNCT
ejpam-2347	149	6	y	y	X
ejpam-2347	149	7	)	)	PUNCT
ejpam-2347	149	8	holds	hold	VERB
ejpam-2347	149	9	for	for	ADP
ejpam-2347	149	10	all	all	PRON
ejpam-2347	149	11	x	x	SYM
ejpam-2347	149	12	,	,	PUNCT
ejpam-2347	149	13	y	y	PROPN
ejpam-2347	149	14	∈	∈	PROPN
ejpam-2347	149	15	zp	zp	PROPN
ejpam-2347	149	16	.	.	PUNCT
ejpam-2347	149	17	proof	proof	NOUN
ejpam-2347	149	18	.	.	PUNCT
ejpam-2347	150	1	in	in	ADP
ejpam-2347	150	2	similar	similar	ADJ
ejpam-2347	150	3	way	way	NOUN
ejpam-2347	150	4	,	,	PUNCT
ejpam-2347	150	5	we	we	PRON
ejpam-2347	150	6	obtain	obtain	VERB
ejpam-2347	150	7	that	that	DET
ejpam-2347	150	8	bp(x	bp(x	PUNCT
ejpam-2347	150	9	+	+	NOUN
ejpam-2347	150	10	1	1	NUM
ejpam-2347	150	11	,	,	PUNCT
ejpam-2347	150	12	y	y	PROPN
ejpam-2347	150	13	+	+	NOUN
ejpam-2347	150	14	1	1	X
ejpam-2347	150	15	)	)	PUNCT
ejpam-2347	150	16	=	=	PRON
ejpam-2347	150	17	γp	γp	PROPN
ejpam-2347	150	18	(	(	PUNCT
ejpam-2347	150	19	x	x	PROPN
ejpam-2347	150	20	+	+	NUM
ejpam-2347	150	21	1)γp(y	1)γp(y	NUM
ejpam-2347	150	22	+	+	NUM
ejpam-2347	150	23	1	1	NUM
ejpam-2347	150	24	)	)	PUNCT
ejpam-2347	150	25	γp(x	γp(x	PUNCT
ejpam-2347	151	1	+	+	NOUN
ejpam-2347	152	1	1	1	NUM
ejpam-2347	152	2	+	+	NUM
ejpam-2347	152	3	y	y	NOUN
ejpam-2347	152	4	+	+	NOUN
ejpam-2347	152	5	1	1	X
ejpam-2347	152	6	)	)	PUNCT
ejpam-2347	152	7	=	=	PRON
ejpam-2347	152	8	γp	γp	PROPN
ejpam-2347	152	9	(	(	PUNCT
ejpam-2347	152	10	x)hp(x)γp(y)hp(y	x)hp(x)γp(y)hp(y	NOUN
ejpam-2347	152	11	)	)	PUNCT
ejpam-2347	152	12	γp((x	γp((x	NOUN
ejpam-2347	153	1	+	+	NOUN
ejpam-2347	153	2	y	y	PROPN
ejpam-2347	154	1	+	+	NOUN
ejpam-2347	154	2	1	1	NUM
ejpam-2347	154	3	)	)	PUNCT
ejpam-2347	154	4	+	+	NOUN
ejpam-2347	154	5	1	1	X
ejpam-2347	154	6	)	)	PUNCT
ejpam-2347	154	7	=	=	PRON
ejpam-2347	154	8	γp	γp	PROPN
ejpam-2347	154	9	(	(	PUNCT
ejpam-2347	154	10	x)hp(x)γp(y)hp(y	x)hp(x)γp(y)hp(y	NOUN
ejpam-2347	154	11	)	)	PUNCT
ejpam-2347	154	12	γp(x	γp(x	PUNCT
ejpam-2347	155	1	+	+	CCONJ
ejpam-2347	155	2	y	y	PROPN
ejpam-2347	155	3	+	+	NOUN
ejpam-2347	155	4	1)hp(x	1)hp(x	NUM
ejpam-2347	156	1	+	+	CCONJ
ejpam-2347	156	2	y	y	PROPN
ejpam-2347	156	3	+	+	CCONJ
ejpam-2347	156	4	1	1	NUM
ejpam-2347	156	5	)	)	PUNCT
ejpam-2347	156	6	=	=	SYM
ejpam-2347	156	7	hp(x)hp(y	hp(x)hp(y	X
ejpam-2347	156	8	)	)	PUNCT
ejpam-2347	156	9	hp(x	hp(x	PROPN
ejpam-2347	157	1	+	+	NOUN
ejpam-2347	157	2	y	y	PROPN
ejpam-2347	157	3	+	+	CCONJ
ejpam-2347	157	4	1	1	X
ejpam-2347	157	5	)	)	PUNCT
ejpam-2347	157	6	γp	γp	NOUN
ejpam-2347	157	7	(	(	PUNCT
ejpam-2347	157	8	x)γp(y	x)γp(y	PROPN
ejpam-2347	157	9	)	)	PUNCT
ejpam-2347	157	10	γp((x	γp((x	NOUN
ejpam-2347	158	1	+	+	CCONJ
ejpam-2347	158	2	y	y	NOUN
ejpam-2347	158	3	)	)	PUNCT
ejpam-2347	159	1	+	+	NOUN
ejpam-2347	159	2	1	1	X
ejpam-2347	159	3	)	)	PUNCT
ejpam-2347	159	4	h.	h.	PROPN
ejpam-2347	159	5	menken	menken	PROPN
ejpam-2347	159	6	,	,	PUNCT
ejpam-2347	159	7	ö.	ö.	VERB
ejpam-2347	159	8	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	159	9	/	/	SYM
ejpam-2347	159	10	eur	eur	PROPN
ejpam-2347	159	11	.	.	PUNCT
ejpam-2347	160	1	j.	j.	PROPN
ejpam-2347	160	2	pure	pure	PROPN
ejpam-2347	160	3	appl	appl	PROPN
ejpam-2347	160	4	.	.	PROPN
ejpam-2347	160	5	math	math	PROPN
ejpam-2347	160	6	,	,	PUNCT
ejpam-2347	160	7	8	8	NUM
ejpam-2347	160	8	(	(	PUNCT
ejpam-2347	160	9	2015	2015	NUM
ejpam-2347	160	10	)	)	PUNCT
ejpam-2347	160	11	,	,	PUNCT
ejpam-2347	160	12	214	214	NUM
ejpam-2347	160	13	-	-	SYM
ejpam-2347	160	14	231	231	NUM
ejpam-2347	160	15	222	222	NUM
ejpam-2347	160	16	=	=	SYM
ejpam-2347	160	17	hp(x)hp(y	hp(x)hp(y	X
ejpam-2347	160	18	)	)	PUNCT
ejpam-2347	160	19	hp(x	hp(x	PROPN
ejpam-2347	161	1	+	+	NOUN
ejpam-2347	161	2	y	y	PROPN
ejpam-2347	161	3	+	+	CCONJ
ejpam-2347	161	4	1	1	X
ejpam-2347	161	5	)	)	PUNCT
ejpam-2347	161	6	γp	γp	NOUN
ejpam-2347	161	7	(	(	PUNCT
ejpam-2347	161	8	x)γp(y	x)γp(y	PROPN
ejpam-2347	161	9	)	)	PUNCT
ejpam-2347	161	10	γp(x	γp(x	PUNCT
ejpam-2347	162	1	+	+	CCONJ
ejpam-2347	163	1	y)hp(x	y)hp(x	PROPN
ejpam-2347	163	2	+	+	NOUN
ejpam-2347	163	3	y	y	NOUN
ejpam-2347	163	4	)	)	PUNCT
ejpam-2347	163	5	=	=	SYM
ejpam-2347	163	6	hp(x)hp(y	hp(x)hp(y	X
ejpam-2347	163	7	)	)	PUNCT
ejpam-2347	163	8	hp(x	hp(x	PROPN
ejpam-2347	164	1	+	+	NOUN
ejpam-2347	164	2	y	y	PROPN
ejpam-2347	164	3	+	+	CCONJ
ejpam-2347	164	4	1)hp(x	1)hp(x	NUM
ejpam-2347	165	1	+	+	CCONJ
ejpam-2347	165	2	y	y	NOUN
ejpam-2347	165	3	)	)	PUNCT
ejpam-2347	165	4	bp(x	bp(x	NOUN
ejpam-2347	165	5	,	,	PUNCT
ejpam-2347	165	6	y	y	PROPN
ejpam-2347	165	7	)	)	PUNCT
ejpam-2347	165	8	.	.	PUNCT
ejpam-2347	166	1	corollary	corollary	ADJ
ejpam-2347	166	2	5	5	NUM
ejpam-2347	166	3	.	.	PUNCT
ejpam-2347	167	1	for	for	ADP
ejpam-2347	167	2	all	all	DET
ejpam-2347	167	3	x	x	SYM
ejpam-2347	167	4	,	,	PUNCT
ejpam-2347	167	5	y	y	PROPN
ejpam-2347	167	6	,	,	PUNCT
ejpam-2347	167	7	z	z	PROPN
ejpam-2347	167	8	∈	∈	PROPN
ejpam-2347	167	9	zp	zp	PROPN
ejpam-2347	167	10	bp(x	bp(x	NOUN
ejpam-2347	167	11	,	,	PUNCT
ejpam-2347	167	12	y)bp(x	y)bp(x	ADJ
ejpam-2347	167	13	+	+	NOUN
ejpam-2347	167	14	y	y	NOUN
ejpam-2347	167	15	,	,	PUNCT
ejpam-2347	167	16	z)bp(x	z)bp(x	X
ejpam-2347	167	17	+	+	NOUN
ejpam-2347	167	18	y	y	PROPN
ejpam-2347	167	19	+	+	PROPN
ejpam-2347	167	20	z	z	PROPN
ejpam-2347	167	21	,	,	PUNCT
ejpam-2347	167	22	w	w	NOUN
ejpam-2347	167	23	)	)	PUNCT
ejpam-2347	167	24	=	=	SYM
ejpam-2347	167	25	γp	γp	PROPN
ejpam-2347	167	26	(	(	PUNCT
ejpam-2347	167	27	x)γp	x)γp	PROPN
ejpam-2347	167	28	�	�	PROPN
ejpam-2347	167	29	y	y	PROPN
ejpam-2347	167	30	�	�	PROPN
ejpam-2347	167	31	γp	γp	PROPN
ejpam-2347	167	32	(	(	PUNCT
ejpam-2347	167	33	z)γp	z)γp	PROPN
ejpam-2347	167	34	(	(	PUNCT
ejpam-2347	167	35	w	w	NOUN
ejpam-2347	167	36	)	)	PUNCT
ejpam-2347	167	37	γp	γp	PROPN
ejpam-2347	167	38	�	�	PROPN
ejpam-2347	167	39	x	x	PUNCT
ejpam-2347	168	1	+	+	PUNCT
ejpam-2347	168	2	y	y	PROPN
ejpam-2347	169	1	+	+	NOUN
ejpam-2347	169	2	z	z	PROPN
ejpam-2347	170	1	+	+	ADJ
ejpam-2347	170	2	w	w	PROPN
ejpam-2347	170	3	�	�	PROPN
ejpam-2347	170	4	proof	proof	NOUN
ejpam-2347	170	5	.	.	PUNCT
ejpam-2347	171	1	it	it	PRON
ejpam-2347	171	2	is	be	AUX
ejpam-2347	171	3	clear	clear	ADJ
ejpam-2347	171	4	from	from	ADP
ejpam-2347	171	5	definition	definition	NOUN
ejpam-2347	171	6	2	2	NUM
ejpam-2347	171	7	that	that	PRON
ejpam-2347	171	8	bp(x	bp(x	NOUN
ejpam-2347	171	9	,	,	PUNCT
ejpam-2347	171	10	y)bp(x	y)bp(x	ADJ
ejpam-2347	171	11	+	+	NOUN
ejpam-2347	171	12	y	y	NOUN
ejpam-2347	171	13	,	,	PUNCT
ejpam-2347	171	14	z)bp(x	z)bp(x	X
ejpam-2347	172	1	+	+	NOUN
ejpam-2347	172	2	y	y	PROPN
ejpam-2347	172	3	+	+	PROPN
ejpam-2347	172	4	z	z	PROPN
ejpam-2347	172	5	,	,	PUNCT
ejpam-2347	172	6	w	w	NOUN
ejpam-2347	172	7	)	)	PUNCT
ejpam-2347	172	8	=	=	SYM
ejpam-2347	172	9	γp	γp	PROPN
ejpam-2347	172	10	(	(	PUNCT
ejpam-2347	172	11	x)γp	x)γp	PROPN
ejpam-2347	172	12	�	�	PROPN
ejpam-2347	172	13	y	y	PROPN
ejpam-2347	172	14	�	�	PROPN
ejpam-2347	172	15	γp	γp	PROPN
ejpam-2347	172	16	�	�	PROPN
ejpam-2347	172	17	x	x	PUNCT
ejpam-2347	173	1	+	+	CCONJ
ejpam-2347	173	2	y	y	PROPN
ejpam-2347	173	3	�	�	PROPN
ejpam-2347	173	4	γp	γp	PROPN
ejpam-2347	173	5	�	�	PROPN
ejpam-2347	173	6	x	x	PUNCT
ejpam-2347	173	7	+	+	CCONJ
ejpam-2347	173	8	y	y	PROPN
ejpam-2347	173	9	�	�	PROPN
ejpam-2347	173	10	γp	γp	PROPN
ejpam-2347	173	11	(	(	PUNCT
ejpam-2347	173	12	z	z	NOUN
ejpam-2347	173	13	)	)	PUNCT
ejpam-2347	173	14	γp	γp	PROPN
ejpam-2347	173	15	�	�	PROPN
ejpam-2347	173	16	x	x	PUNCT
ejpam-2347	174	1	+	+	CCONJ
ejpam-2347	174	2	y	y	PROPN
ejpam-2347	174	3	+	+	CCONJ
ejpam-2347	174	4	z	z	PROPN
ejpam-2347	174	5	�	�	PROPN
ejpam-2347	174	6	γp	γp	PROPN
ejpam-2347	174	7	�	�	PROPN
ejpam-2347	174	8	x	x	PUNCT
ejpam-2347	175	1	+	+	CCONJ
ejpam-2347	175	2	y	y	PROPN
ejpam-2347	175	3	+	+	CCONJ
ejpam-2347	175	4	z	z	PROPN
ejpam-2347	175	5	�	�	PROPN
ejpam-2347	175	6	γp	γp	PROPN
ejpam-2347	175	7	(	(	PUNCT
ejpam-2347	175	8	w	w	NOUN
ejpam-2347	175	9	)	)	PUNCT
ejpam-2347	175	10	γp	γp	PROPN
ejpam-2347	175	11	�	�	PROPN
ejpam-2347	175	12	x	x	PUNCT
ejpam-2347	176	1	+	+	PUNCT
ejpam-2347	176	2	y	y	PROPN
ejpam-2347	177	1	+	+	NOUN
ejpam-2347	177	2	z	z	PROPN
ejpam-2347	178	1	+	+	PROPN
ejpam-2347	178	2	w	w	PROPN
ejpam-2347	178	3	�	�	PROPN
ejpam-2347	178	4	=	=	SYM
ejpam-2347	178	5	γp	γp	PROPN
ejpam-2347	178	6	(	(	PUNCT
ejpam-2347	178	7	x)γp	x)γp	PROPN
ejpam-2347	178	8	�	�	PROPN
ejpam-2347	178	9	y	y	PROPN
ejpam-2347	178	10	�	�	PROPN
ejpam-2347	178	11	γp	γp	PROPN
ejpam-2347	178	12	(	(	PUNCT
ejpam-2347	178	13	z)γp	z)γp	PROPN
ejpam-2347	178	14	(	(	PUNCT
ejpam-2347	178	15	w	w	NOUN
ejpam-2347	178	16	)	)	PUNCT
ejpam-2347	178	17	γp	γp	PROPN
ejpam-2347	178	18	�	�	PROPN
ejpam-2347	178	19	x	x	PUNCT
ejpam-2347	179	1	+	+	PUNCT
ejpam-2347	179	2	y	y	PROPN
ejpam-2347	180	1	+	+	NOUN
ejpam-2347	180	2	z	z	PROPN
ejpam-2347	181	1	+	+	PROPN
ejpam-2347	181	2	w	w	PROPN
ejpam-2347	181	3	�	�	PROPN
ejpam-2347	181	4	.	.	PUNCT
ejpam-2347	182	1	theorem	theorem	VERB
ejpam-2347	182	2	6	6	NUM
ejpam-2347	182	3	.	.	PUNCT
ejpam-2347	183	1	the	the	DET
ejpam-2347	183	2	equality	equality	NOUN
ejpam-2347	183	3	bp(x	bp(x	NOUN
ejpam-2347	183	4	,	,	PUNCT
ejpam-2347	183	5	1−	1−	NUM
ejpam-2347	183	6	x	x	X
ejpam-2347	183	7	)	)	PUNCT
ejpam-2347	184	1	=	=	SYM
ejpam-2347	184	2	¨	¨	NOUN
ejpam-2347	184	3	(	(	PUNCT
ejpam-2347	184	4	−1)ℓ(x)+1	−1)ℓ(x)+1	NOUN
ejpam-2347	184	5	if	if	SCONJ
ejpam-2347	184	6	p	p	PROPN
ejpam-2347	184	7	6=	6=	NUM
ejpam-2347	184	8	2	2	NUM
ejpam-2347	184	9	(	(	PUNCT
ejpam-2347	184	10	−1)σ1(y)+2	−1)σ1(y)+2	PROPN
ejpam-2347	184	11	if	if	SCONJ
ejpam-2347	184	12	p	p	NOUN
ejpam-2347	184	13	=	=	SYM
ejpam-2347	184	14	2	2	NUM
ejpam-2347	184	15	holds	hold	VERB
ejpam-2347	184	16	for	for	ADP
ejpam-2347	184	17	all	all	DET
ejpam-2347	184	18	x	x	SYM
ejpam-2347	184	19	,	,	PUNCT
ejpam-2347	184	20	y	y	PROPN
ejpam-2347	184	21	∈	∈	PROPN
ejpam-2347	184	22	zp	zp	PROPN
ejpam-2347	184	23	.	.	PUNCT
ejpam-2347	184	24	proof	proof	NOUN
ejpam-2347	184	25	.	.	PUNCT
ejpam-2347	185	1	note	note	VERB
ejpam-2347	185	2	that	that	SCONJ
ejpam-2347	185	3	γp(1	γp(1	NOUN
ejpam-2347	185	4	)	)	PUNCT
ejpam-2347	185	5	=	=	SYM
ejpam-2347	185	6	−1	−1	NOUN
ejpam-2347	185	7	.	.	PUNCT
ejpam-2347	186	1	by	by	ADP
ejpam-2347	186	2	definition	definition	NOUN
ejpam-2347	186	3	2	2	NUM
ejpam-2347	186	4	we	we	PRON
ejpam-2347	186	5	get	get	VERB
ejpam-2347	186	6	bp(x	bp(x	NOUN
ejpam-2347	186	7	,	,	PUNCT
ejpam-2347	186	8	1−	1−	NUM
ejpam-2347	186	9	x	x	X
ejpam-2347	186	10	)	)	PUNCT
ejpam-2347	186	11	=	=	SYM
ejpam-2347	186	12	γp	γp	PROPN
ejpam-2347	186	13	(	(	PUNCT
ejpam-2347	186	14	x)γp(1−	x)γp(1−	NOUN
ejpam-2347	186	15	x	x	X
ejpam-2347	186	16	)	)	PUNCT
ejpam-2347	186	17	γp(x	γp(x	PUNCT
ejpam-2347	187	1	+	+	NOUN
ejpam-2347	187	2	1−	1−	NUM
ejpam-2347	187	3	x	x	X
ejpam-2347	187	4	)	)	PUNCT
ejpam-2347	187	5	=	=	SYM
ejpam-2347	187	6	γp	γp	PROPN
ejpam-2347	187	7	(	(	PUNCT
ejpam-2347	187	8	x)γp(1−	x)γp(1−	NOUN
ejpam-2347	187	9	x	x	X
ejpam-2347	187	10	)	)	PUNCT
ejpam-2347	187	11	γp(1	γp(1	NOUN
ejpam-2347	187	12	)	)	PUNCT
ejpam-2347	187	13	.	.	PUNCT
ejpam-2347	188	1	by	by	ADP
ejpam-2347	188	2	proposition	proposition	NOUN
ejpam-2347	188	3	3	3	NUM
ejpam-2347	188	4	,	,	PUNCT
ejpam-2347	188	5	if	if	SCONJ
ejpam-2347	188	6	p	p	X
ejpam-2347	188	7	6=	6=	NUM
ejpam-2347	188	8	2	2	NUM
ejpam-2347	188	9	then	then	ADV
ejpam-2347	188	10	bp(x	bp(x	NOUN
ejpam-2347	188	11	,	,	PUNCT
ejpam-2347	188	12	1−	1−	NUM
ejpam-2347	188	13	x	x	X
ejpam-2347	188	14	)	)	PUNCT
ejpam-2347	188	15	=	=	SYM
ejpam-2347	188	16	−(−1)ℓ(x	−(−1)ℓ(x	NOUN
ejpam-2347	188	17	)	)	PUNCT
ejpam-2347	188	18	=	=	PRON
ejpam-2347	188	19	(	(	PUNCT
ejpam-2347	188	20	−1)ℓ(x)+1	−1)ℓ(x)+1	NUM
ejpam-2347	188	21	and	and	CCONJ
ejpam-2347	188	22	,	,	PUNCT
ejpam-2347	188	23	if	if	SCONJ
ejpam-2347	188	24	p	p	NOUN
ejpam-2347	188	25	=	=	NOUN
ejpam-2347	188	26	2	2	NUM
ejpam-2347	188	27	then	then	ADV
ejpam-2347	188	28	,	,	PUNCT
ejpam-2347	188	29	bp(x	bp(x	NOUN
ejpam-2347	188	30	,	,	PUNCT
ejpam-2347	188	31	1−	1−	NUM
ejpam-2347	188	32	x	x	X
ejpam-2347	188	33	)	)	PUNCT
ejpam-2347	188	34	=	=	SYM
ejpam-2347	188	35	−(−1)σ1(y)+1	−(−1)σ1(y)+1	NOUN
ejpam-2347	188	36	=	=	SYM
ejpam-2347	188	37	(	(	PUNCT
ejpam-2347	188	38	−1	−1	NOUN
ejpam-2347	188	39	)	)	PUNCT
ejpam-2347	188	40	σ1(y)+2	σ1(y)+2	NOUN
ejpam-2347	188	41	.	.	PUNCT
ejpam-2347	189	1	it	it	PRON
ejpam-2347	189	2	is	be	AUX
ejpam-2347	189	3	well	well	ADV
ejpam-2347	189	4	known	know	VERB
ejpam-2347	189	5	that	that	SCONJ
ejpam-2347	189	6	the	the	DET
ejpam-2347	189	7	classical	classical	ADJ
ejpam-2347	189	8	beta	beta	NOUN
ejpam-2347	189	9	function	function	NOUN
ejpam-2347	189	10	can	can	AUX
ejpam-2347	189	11	be	be	AUX
ejpam-2347	189	12	defined	define	VERB
ejpam-2347	189	13	as	as	ADP
ejpam-2347	189	14	binomial	binomial	ADJ
ejpam-2347	189	15	coefficient	coefficient	NOUN
ejpam-2347	189	16	indices	index	NOUN
ejpam-2347	189	17	.	.	PUNCT
ejpam-2347	190	1	we	we	PRON
ejpam-2347	190	2	can	can	AUX
ejpam-2347	190	3	give	give	VERB
ejpam-2347	190	4	a	a	DET
ejpam-2347	190	5	similar	similar	ADJ
ejpam-2347	190	6	formula	formula	NOUN
ejpam-2347	190	7	for	for	ADP
ejpam-2347	190	8	the	the	DET
ejpam-2347	190	9	p	p	NOUN
ejpam-2347	190	10	-	-	PUNCT
ejpam-2347	190	11	adic	adic	ADJ
ejpam-2347	190	12	beta	beta	NOUN
ejpam-2347	190	13	function	function	NOUN
ejpam-2347	190	14	.	.	PUNCT
ejpam-2347	191	1	h.	h.	PROPN
ejpam-2347	191	2	menken	menken	PROPN
ejpam-2347	191	3	,	,	PUNCT
ejpam-2347	191	4	ö.	ö.	VERB
ejpam-2347	191	5	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	191	6	/	/	SYM
ejpam-2347	191	7	eur	eur	PROPN
ejpam-2347	191	8	.	.	PUNCT
ejpam-2347	192	1	j.	j.	PROPN
ejpam-2347	192	2	pure	pure	PROPN
ejpam-2347	192	3	appl	appl	PROPN
ejpam-2347	192	4	.	.	PROPN
ejpam-2347	192	5	math	math	PROPN
ejpam-2347	192	6	,	,	PUNCT
ejpam-2347	192	7	8	8	NUM
ejpam-2347	192	8	(	(	PUNCT
ejpam-2347	192	9	2015	2015	NUM
ejpam-2347	192	10	)	)	PUNCT
ejpam-2347	192	11	,	,	PUNCT
ejpam-2347	192	12	214	214	NUM
ejpam-2347	192	13	-	-	SYM
ejpam-2347	192	14	231	231	NUM
ejpam-2347	192	15	223	223	NUM
ejpam-2347	192	16	theorem	theorem	NOUN
ejpam-2347	192	17	7	7	NUM
ejpam-2347	192	18	.	.	PUNCT
ejpam-2347	193	1	the	the	DET
ejpam-2347	193	2	equality	equality	NOUN
ejpam-2347	193	3	�	�	PROPN
ejpam-2347	193	4	n	n	CCONJ
ejpam-2347	193	5	k	k	PROPN
ejpam-2347	193	6	�	�	PROPN
ejpam-2347	193	7	p	p	PROPN
ejpam-2347	193	8	bp(n−	bp(n−	PROPN
ejpam-2347	193	9	k+	k+	NOUN
ejpam-2347	193	10	1	1	NUM
ejpam-2347	193	11	,	,	PUNCT
ejpam-2347	193	12	k+	k+	NOUN
ejpam-2347	193	13	1	1	NUM
ejpam-2347	193	14	)	)	PUNCT
ejpam-2347	193	15	=	=	VERB
ejpam-2347	193	16	−1	−1	NOUN
ejpam-2347	193	17	hp(n+	hp(n+	NUM
ejpam-2347	193	18	1	1	NUM
ejpam-2347	193	19	)	)	PUNCT
ejpam-2347	193	20	holds	hold	VERB
ejpam-2347	193	21	for	for	ADP
ejpam-2347	193	22	all	all	DET
ejpam-2347	193	23	n	n	NOUN
ejpam-2347	193	24	,	,	PUNCT
ejpam-2347	193	25	k	k	PROPN
ejpam-2347	193	26	∈	∈	PROPN
ejpam-2347	193	27	n	n	CCONJ
ejpam-2347	193	28	,	,	PUNCT
ejpam-2347	193	29	k	k	PROPN
ejpam-2347	193	30	≤	≤	PROPN
ejpam-2347	193	31	n.	n.	NOUN
ejpam-2347	193	32	here	here	ADV
ejpam-2347	193	33	,	,	PUNCT
ejpam-2347	193	34	the	the	DET
ejpam-2347	193	35	notation	notation	NOUN
ejpam-2347	193	36	�	�	PROPN
ejpam-2347	193	37	n	n	CCONJ
ejpam-2347	193	38	k	k	PROPN
ejpam-2347	193	39	�	�	PROPN
ejpam-2347	193	40	p	p	PROPN
ejpam-2347	193	41	is	be	AUX
ejpam-2347	193	42	defined	define	VERB
ejpam-2347	193	43	by	by	ADP
ejpam-2347	193	44	�	�	PROPN
ejpam-2347	193	45	n	n	CCONJ
ejpam-2347	193	46	k	k	PROPN
ejpam-2347	193	47	�	�	PROPN
ejpam-2347	193	48	p	p	NOUN
ejpam-2347	193	49	=	=	X
ejpam-2347	193	50	(	(	PUNCT
ejpam-2347	193	51	n!)p	n!)p	X
ejpam-2347	193	52	(	(	PUNCT
ejpam-2347	193	53	(	(	PUNCT
ejpam-2347	193	54	n−	n−	NOUN
ejpam-2347	193	55	k)!)p(k!)p	k)!)p(k!)p	NOUN
ejpam-2347	193	56	.	.	PUNCT
ejpam-2347	194	1	proof	proof	NOUN
ejpam-2347	194	2	.	.	PUNCT
ejpam-2347	195	1	it	it	PRON
ejpam-2347	195	2	is	be	AUX
ejpam-2347	195	3	well	well	ADV
ejpam-2347	195	4	known	know	VERB
ejpam-2347	195	5	that	that	SCONJ
ejpam-2347	195	6	�	�	PROPN
ejpam-2347	195	7	n	n	CCONJ
ejpam-2347	195	8	k	k	PROPN
ejpam-2347	195	9	�	�	PROPN
ejpam-2347	195	10	=	=	SYM
ejpam-2347	195	11	n	n	X
ejpam-2347	195	12	!	!	PUNCT
ejpam-2347	196	1	(	(	PUNCT
ejpam-2347	196	2	n−	n−	NOUN
ejpam-2347	196	3	k)!k	k)!k	PROPN
ejpam-2347	196	4	!	!	PUNCT
ejpam-2347	197	1	for	for	ADP
ejpam-2347	197	2	n	n	PRON
ejpam-2347	197	3	,	,	PUNCT
ejpam-2347	197	4	k	k	PROPN
ejpam-2347	197	5	∈	∈	PROPN
ejpam-2347	197	6	n	n	CCONJ
ejpam-2347	197	7	,	,	PUNCT
ejpam-2347	197	8	k	k	PROPN
ejpam-2347	197	9	≤	≤	PROPN
ejpam-2347	197	10	n	n	CCONJ
ejpam-2347	197	11	and	and	CCONJ
ejpam-2347	197	12	(	(	PUNCT
ejpam-2347	197	13	n!)p	n!)p	NOUN
ejpam-2347	197	14	=	=	SYM
ejpam-2347	197	15	(	(	PUNCT
ejpam-2347	197	16	−1)n+1γp(n+	−1)n+1γp(n+	ADP
ejpam-2347	197	17	1	1	NUM
ejpam-2347	197	18	)	)	PUNCT
ejpam-2347	197	19	.	.	PUNCT
ejpam-2347	198	1	hence	hence	ADV
ejpam-2347	198	2	,	,	PUNCT
ejpam-2347	198	3	we	we	PRON
ejpam-2347	198	4	can	can	AUX
ejpam-2347	198	5	write	write	VERB
ejpam-2347	198	6	�	�	PROPN
ejpam-2347	198	7	n	n	CCONJ
ejpam-2347	198	8	k	k	PROPN
ejpam-2347	198	9	�	�	PROPN
ejpam-2347	198	10	p	p	PROPN
ejpam-2347	198	11	bp(n−	bp(n−	PROPN
ejpam-2347	198	12	k+	k+	NOUN
ejpam-2347	198	13	1	1	NUM
ejpam-2347	198	14	,	,	PUNCT
ejpam-2347	198	15	k+	k+	NOUN
ejpam-2347	198	16	1	1	NUM
ejpam-2347	198	17	)	)	PUNCT
ejpam-2347	198	18	=	=	SYM
ejpam-2347	198	19	(	(	PUNCT
ejpam-2347	198	20	n!)p	n!)p	X
ejpam-2347	198	21	(	(	PUNCT
ejpam-2347	198	22	k!)p((n−	k!)p((n−	PROPN
ejpam-2347	198	23	k)!)p	k)!)p	PROPN
ejpam-2347	198	24	γp	γp	PROPN
ejpam-2347	198	25	(	(	PUNCT
ejpam-2347	198	26	n−	n−	NOUN
ejpam-2347	198	27	k+	k+	NOUN
ejpam-2347	198	28	1)γp(k+	1)γp(k+	ADJ
ejpam-2347	198	29	1	1	NUM
ejpam-2347	198	30	)	)	PUNCT
ejpam-2347	198	31	γp(n+	γp(n+	ADP
ejpam-2347	198	32	2	2	X
ejpam-2347	198	33	)	)	PUNCT
ejpam-2347	198	34	=	=	SYM
ejpam-2347	198	35	(	(	PUNCT
ejpam-2347	198	36	−1)n+1γp	−1)n+1γp	X
ejpam-2347	198	37	(	(	PUNCT
ejpam-2347	198	38	n+	n+	NOUN
ejpam-2347	198	39	1	1	NUM
ejpam-2347	198	40	)	)	PUNCT
ejpam-2347	198	41	(	(	PUNCT
ejpam-2347	198	42	−1)k+1γp(k+	−1)k+1γp(k+	PROPN
ejpam-2347	198	43	1)(−1)n−k+1γp(n−	1)(−1)n−k+1γp(n−	NUM
ejpam-2347	198	44	k+	k+	NOUN
ejpam-2347	198	45	1	1	NUM
ejpam-2347	198	46	)	)	PUNCT
ejpam-2347	198	47	γp	γp	NOUN
ejpam-2347	198	48	(	(	PUNCT
ejpam-2347	198	49	n−	n−	NOUN
ejpam-2347	198	50	k+	k+	NOUN
ejpam-2347	198	51	1)γp(k+	1)γp(k+	ADJ
ejpam-2347	198	52	1	1	NUM
ejpam-2347	198	53	)	)	PUNCT
ejpam-2347	198	54	γp(n+	γp(n+	ADP
ejpam-2347	198	55	2	2	X
ejpam-2347	198	56	)	)	PUNCT
ejpam-2347	198	57	=	=	PRON
ejpam-2347	198	58	−γp	−γp	X
ejpam-2347	198	59	(	(	PUNCT
ejpam-2347	198	60	n+	n+	NOUN
ejpam-2347	198	61	1	1	NUM
ejpam-2347	198	62	)	)	PUNCT
ejpam-2347	198	63	γp(n+	γp(n+	ADP
ejpam-2347	198	64	2	2	NUM
ejpam-2347	198	65	)	)	PUNCT
ejpam-2347	198	66	.	.	PUNCT
ejpam-2347	199	1	thus	thus	ADV
ejpam-2347	199	2	,	,	PUNCT
ejpam-2347	199	3	by	by	ADP
ejpam-2347	199	4	proposition	proposition	NOUN
ejpam-2347	199	5	1	1	NUM
ejpam-2347	199	6	,	,	PUNCT
ejpam-2347	199	7	we	we	PRON
ejpam-2347	199	8	obtain	obtain	VERB
ejpam-2347	199	9	that	that	SCONJ
ejpam-2347	199	10	�	�	PROPN
ejpam-2347	199	11	n	n	CCONJ
ejpam-2347	199	12	k	k	PROPN
ejpam-2347	199	13	�	�	PROPN
ejpam-2347	199	14	p	p	PROPN
ejpam-2347	199	15	bp(n−	bp(n−	PROPN
ejpam-2347	199	16	k+	k+	NOUN
ejpam-2347	199	17	1	1	NUM
ejpam-2347	199	18	,	,	PUNCT
ejpam-2347	199	19	k+	k+	NOUN
ejpam-2347	199	20	1	1	X
ejpam-2347	199	21	)	)	PUNCT
ejpam-2347	200	1	=	=	PRON
ejpam-2347	200	2	−γp	−γp	X
ejpam-2347	200	3	(	(	PUNCT
ejpam-2347	200	4	n+	n+	NOUN
ejpam-2347	200	5	1	1	NUM
ejpam-2347	200	6	)	)	PUNCT
ejpam-2347	200	7	γp(n+	γp(n+	ADP
ejpam-2347	200	8	1)hp(n+	1)hp(n+	ADV
ejpam-2347	200	9	1	1	NUM
ejpam-2347	200	10	)	)	PUNCT
ejpam-2347	200	11	=	=	VERB
ejpam-2347	201	1	−1	−1	NOUN
ejpam-2347	201	2	hp(n+	hp(n+	PROPN
ejpam-2347	201	3	1	1	NUM
ejpam-2347	201	4	)	)	PUNCT
ejpam-2347	201	5	.	.	PUNCT
ejpam-2347	202	1	now	now	ADV
ejpam-2347	202	2	,	,	PUNCT
ejpam-2347	202	3	we	we	PRON
ejpam-2347	202	4	analyze	analyze	VERB
ejpam-2347	202	5	the	the	DET
ejpam-2347	202	6	relationship	relationship	NOUN
ejpam-2347	202	7	between	between	ADP
ejpam-2347	202	8	the	the	DET
ejpam-2347	202	9	classical	classical	ADJ
ejpam-2347	202	10	beta	beta	NOUN
ejpam-2347	202	11	and	and	CCONJ
ejpam-2347	202	12	the	the	DET
ejpam-2347	202	13	p	p	NOUN
ejpam-2347	202	14	-	-	PUNCT
ejpam-2347	202	15	adic	adic	ADJ
ejpam-2347	202	16	beta	beta	NOUN
ejpam-2347	202	17	function	function	NOUN
ejpam-2347	202	18	at	at	ADP
ejpam-2347	202	19	the	the	DET
ejpam-2347	202	20	values	value	NOUN
ejpam-2347	202	21	of	of	ADP
ejpam-2347	202	22	natural	natural	ADJ
ejpam-2347	202	23	numbers	number	NOUN
ejpam-2347	202	24	.	.	PUNCT
ejpam-2347	203	1	theorem	theorem	VERB
ejpam-2347	203	2	8	8	NUM
ejpam-2347	203	3	.	.	PUNCT
ejpam-2347	204	1	the	the	DET
ejpam-2347	204	2	equality	equality	NOUN
ejpam-2347	204	3	b(n+	b(n+	NOUN
ejpam-2347	204	4	1	1	NUM
ejpam-2347	204	5	,	,	PUNCT
ejpam-2347	204	6	m+	m+	NOUN
ejpam-2347	204	7	1	1	NUM
ejpam-2347	204	8	)	)	PUNCT
ejpam-2347	204	9	=	=	SYM
ejpam-2347	204	10	−bp(n	−bp(n	PROPN
ejpam-2347	204	11	,	,	PUNCT
ejpam-2347	204	12	m	m	NOUN
ejpam-2347	204	13	)	)	PUNCT
ejpam-2347	204	14	hp(n)hp(m	hp(n)hp(m	ADV
ejpam-2347	204	15	)	)	PUNCT
ejpam-2347	204	16	hp(m+	hp(m+	NOUN
ejpam-2347	204	17	n)(m+	n)(m+	NUM
ejpam-2347	204	18	n+	n+	NUM
ejpam-2347	204	19	1	1	NUM
ejpam-2347	204	20	)	)	PUNCT
ejpam-2347	204	21	�	�	PROPN
ejpam-2347	204	22	n	n	CCONJ
ejpam-2347	204	23	p	p	PROPN
ejpam-2347	204	24	�	�	PROPN
ejpam-2347	204	25	!	!	PUNCT
ejpam-2347	205	1	�	�	PROPN
ejpam-2347	205	2	m	m	PROPN
ejpam-2347	205	3	p	p	PROPN
ejpam-2347	205	4	�	�	PROPN
ejpam-2347	205	5	!	!	PUNCT
ejpam-2347	206	1	�	�	PROPN
ejpam-2347	206	2	m+n	m+n	PROPN
ejpam-2347	206	3	p	p	PROPN
ejpam-2347	206	4	�	�	PROPN
ejpam-2347	206	5	!	!	PUNCT
ejpam-2347	207	1	p	p	PRON
ejpam-2347	207	2	�	�	PROPN
ejpam-2347	207	3	n	n	CCONJ
ejpam-2347	207	4	p	p	PROPN
ejpam-2347	207	5	�	�	PROPN
ejpam-2347	207	6	+	+	CCONJ
ejpam-2347	207	7	�	�	PROPN
ejpam-2347	207	8	m	m	PROPN
ejpam-2347	207	9	p	p	PROPN
ejpam-2347	207	10	�	�	PROPN
ejpam-2347	207	11	−	−	PROPN
ejpam-2347	207	12	�	�	PROPN
ejpam-2347	207	13	m+n	m+n	PROPN
ejpam-2347	207	14	p	p	PROPN
ejpam-2347	207	15	�	�	PROPN
ejpam-2347	207	16	holds	hold	VERB
ejpam-2347	207	17	for	for	ADP
ejpam-2347	207	18	all	all	DET
ejpam-2347	207	19	m	m	NOUN
ejpam-2347	207	20	,	,	PUNCT
ejpam-2347	207	21	n	n	PROPN
ejpam-2347	207	22	∈	∈	PROPN
ejpam-2347	207	23	n.	n.	PROPN
ejpam-2347	207	24	h.	h.	PROPN
ejpam-2347	207	25	menken	menken	PROPN
ejpam-2347	207	26	,	,	PUNCT
ejpam-2347	207	27	ö.	ö.	VERB
ejpam-2347	207	28	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	207	29	/	/	SYM
ejpam-2347	207	30	eur	eur	PROPN
ejpam-2347	207	31	.	.	PUNCT
ejpam-2347	208	1	j.	j.	PROPN
ejpam-2347	208	2	pure	pure	PROPN
ejpam-2347	208	3	appl	appl	PROPN
ejpam-2347	208	4	.	.	PROPN
ejpam-2347	208	5	math	math	PROPN
ejpam-2347	208	6	,	,	PUNCT
ejpam-2347	208	7	8	8	NUM
ejpam-2347	208	8	(	(	PUNCT
ejpam-2347	208	9	2015	2015	NUM
ejpam-2347	208	10	)	)	PUNCT
ejpam-2347	208	11	,	,	PUNCT
ejpam-2347	208	12	214	214	NUM
ejpam-2347	208	13	-	-	SYM
ejpam-2347	208	14	231	231	NUM
ejpam-2347	208	15	224	224	NUM
ejpam-2347	208	16	proof	proof	NOUN
ejpam-2347	208	17	.	.	PUNCT
ejpam-2347	209	1	it	it	PRON
ejpam-2347	209	2	follows	follow	VERB
ejpam-2347	209	3	from	from	ADP
ejpam-2347	209	4	the	the	DET
ejpam-2347	209	5	definition	definition	NOUN
ejpam-2347	209	6	of	of	ADP
ejpam-2347	209	7	classical	classical	ADJ
ejpam-2347	209	8	beta	beta	NOUN
ejpam-2347	209	9	function	function	NOUN
ejpam-2347	209	10	and	and	CCONJ
ejpam-2347	209	11	main	main	ADJ
ejpam-2347	209	12	proposition	proposition	NOUN
ejpam-2347	209	13	of	of	ADP
ejpam-2347	209	14	classical	classical	ADJ
ejpam-2347	209	15	gamma	gamma	NOUN
ejpam-2347	209	16	function	function	NOUN
ejpam-2347	209	17	that	that	SCONJ
ejpam-2347	209	18	b(n+	b(n+	PROPN
ejpam-2347	209	19	1	1	NUM
ejpam-2347	209	20	,	,	PUNCT
ejpam-2347	209	21	m+	m+	NOUN
ejpam-2347	209	22	1	1	NUM
ejpam-2347	209	23	)	)	PUNCT
ejpam-2347	209	24	=	=	PUNCT
ejpam-2347	209	25	γ(n+	γ(n+	NUM
ejpam-2347	210	1	1)γ(m+	1)γ(m+	NUM
ejpam-2347	210	2	1	1	NUM
ejpam-2347	210	3	)	)	PUNCT
ejpam-2347	210	4	γ(n+m+	γ(n+m+	PUNCT
ejpam-2347	211	1	2	2	X
ejpam-2347	211	2	)	)	PUNCT
ejpam-2347	211	3	=	=	PUNCT
ejpam-2347	211	4	γ(n+	γ(n+	NUM
ejpam-2347	211	5	1)γ(m+	1)γ(m+	NUM
ejpam-2347	211	6	1	1	NUM
ejpam-2347	211	7	)	)	PUNCT
ejpam-2347	211	8	(	(	PUNCT
ejpam-2347	211	9	n+m+	n+m+	X
ejpam-2347	211	10	1)γ(m+	1)γ(m+	NUM
ejpam-2347	211	11	n+	n+	NOUN
ejpam-2347	211	12	1	1	NUM
ejpam-2347	211	13	)	)	PUNCT
ejpam-2347	211	14	=	=	SYM
ejpam-2347	211	15	n!m	n!m	PROPN
ejpam-2347	211	16	!	!	PUNCT
ejpam-2347	212	1	(	(	PUNCT
ejpam-2347	212	2	n+m+	n+m+	X
ejpam-2347	212	3	1)(m+	1)(m+	NUM
ejpam-2347	212	4	n	n	CCONJ
ejpam-2347	212	5	)	)	PUNCT
ejpam-2347	212	6	!	!	PUNCT
ejpam-2347	212	7	.	.	PUNCT
ejpam-2347	213	1	by	by	ADP
ejpam-2347	213	2	proposition	proposition	NOUN
ejpam-2347	213	3	4(i	4(i	NUM
ejpam-2347	213	4	)	)	PUNCT
ejpam-2347	214	1	we	we	PRON
ejpam-2347	214	2	have	have	VERB
ejpam-2347	214	3	b(n+	b(n+	NOUN
ejpam-2347	214	4	1	1	NUM
ejpam-2347	214	5	,	,	PUNCT
ejpam-2347	214	6	m+	m+	NOUN
ejpam-2347	214	7	1	1	NUM
ejpam-2347	214	8	)	)	PUNCT
ejpam-2347	214	9	=	=	NOUN
ejpam-2347	214	10	(	(	PUNCT
ejpam-2347	214	11	−1)n+1γp(n+	−1)n+1γp(n+	ADP
ejpam-2347	214	12	1	1	NUM
ejpam-2347	214	13	)	)	PUNCT
ejpam-2347	214	14	�	�	PROPN
ejpam-2347	214	15	n	n	CCONJ
ejpam-2347	214	16	p	p	PROPN
ejpam-2347	214	17	�	�	PROPN
ejpam-2347	214	18	!	!	PUNCT
ejpam-2347	215	1	p	p	PROPN
ejpam-2347	215	2	�	�	PROPN
ejpam-2347	215	3	n	n	CCONJ
ejpam-2347	215	4	p	p	PROPN
ejpam-2347	215	5	�	�	PROPN
ejpam-2347	215	6	(	(	PUNCT
ejpam-2347	215	7	−1)m+1γp(m+	−1)m+1γp(m+	PROPN
ejpam-2347	215	8	1	1	NUM
ejpam-2347	215	9	)	)	PUNCT
ejpam-2347	215	10	�	�	PROPN
ejpam-2347	215	11	m	m	PROPN
ejpam-2347	215	12	p	p	NOUN
ejpam-2347	215	13	�	�	PROPN
ejpam-2347	215	14	!	!	PUNCT
ejpam-2347	216	1	p	p	PROPN
ejpam-2347	216	2	�	�	PROPN
ejpam-2347	216	3	m	m	PROPN
ejpam-2347	216	4	p	p	PROPN
ejpam-2347	216	5	�	�	PROPN
ejpam-2347	216	6	(	(	PUNCT
ejpam-2347	216	7	n+m+	n+m+	X
ejpam-2347	216	8	1)(−1)m+n+1γp(m+	1)(−1)m+n+1γp(m+	NUM
ejpam-2347	216	9	n+	n+	ADP
ejpam-2347	216	10	1	1	NUM
ejpam-2347	216	11	)	)	PUNCT
ejpam-2347	216	12	�	�	PROPN
ejpam-2347	216	13	m+n	m+n	PROPN
ejpam-2347	217	1	p	p	PROPN
ejpam-2347	217	2	�	�	PROPN
ejpam-2347	217	3	!	!	PUNCT
ejpam-2347	218	1	p	p	PROPN
ejpam-2347	218	2	�	�	PROPN
ejpam-2347	218	3	m+n	m+n	PROPN
ejpam-2347	219	1	p	p	PROPN
ejpam-2347	219	2	�	�	PROPN
ejpam-2347	219	3	.	.	PUNCT
ejpam-2347	220	1	then	then	ADV
ejpam-2347	220	2	,	,	PUNCT
ejpam-2347	220	3	by	by	ADP
ejpam-2347	220	4	proposition	proposition	NOUN
ejpam-2347	220	5	1	1	NUM
ejpam-2347	220	6	we	we	PRON
ejpam-2347	220	7	obtain	obtain	VERB
ejpam-2347	220	8	b(n+	b(n+	NOUN
ejpam-2347	220	9	1	1	NUM
ejpam-2347	220	10	,	,	PUNCT
ejpam-2347	220	11	m+	m+	NOUN
ejpam-2347	220	12	1	1	NUM
ejpam-2347	220	13	)	)	PUNCT
ejpam-2347	220	14	=	=	PRON
ejpam-2347	220	15	(	(	PUNCT
ejpam-2347	220	16	−1	−1	NOUN
ejpam-2347	220	17	)	)	PUNCT
ejpam-2347	220	18	γp(n)γp(m)hp(n)hp(m	γp(n)γp(m)hp(n)hp(m	PROPN
ejpam-2347	220	19	)	)	PUNCT
ejpam-2347	220	20	γp(n+m)hp(n+m	γp(n+m)hp(n+m	PROPN
ejpam-2347	220	21	)	)	PUNCT
ejpam-2347	220	22	�	�	PROPN
ejpam-2347	220	23	n	n	CCONJ
ejpam-2347	220	24	p	p	PROPN
ejpam-2347	220	25	�	�	PROPN
ejpam-2347	220	26	!	!	PUNCT
ejpam-2347	221	1	�	�	PROPN
ejpam-2347	221	2	m	m	PROPN
ejpam-2347	221	3	p	p	PROPN
ejpam-2347	221	4	�	�	PROPN
ejpam-2347	221	5	!	!	PUNCT
ejpam-2347	222	1	�	�	PROPN
ejpam-2347	222	2	m+n	m+n	PROPN
ejpam-2347	222	3	p	p	PROPN
ejpam-2347	222	4	�	�	PROPN
ejpam-2347	222	5	!	!	PUNCT
ejpam-2347	223	1	p	p	PRON
ejpam-2347	223	2	�	�	PROPN
ejpam-2347	223	3	n	n	CCONJ
ejpam-2347	223	4	p	p	PROPN
ejpam-2347	223	5	�	�	PROPN
ejpam-2347	223	6	+	+	CCONJ
ejpam-2347	223	7	�	�	PROPN
ejpam-2347	223	8	m	m	PROPN
ejpam-2347	223	9	p	p	PROPN
ejpam-2347	223	10	�	�	PROPN
ejpam-2347	223	11	−	−	PROPN
ejpam-2347	223	12	�	�	PROPN
ejpam-2347	223	13	m+n	m+n	PROPN
ejpam-2347	224	1	p	p	PROPN
ejpam-2347	225	1	�	�	PROPN
ejpam-2347	226	1	(	(	PUNCT
ejpam-2347	226	2	n+m+	n+m+	X
ejpam-2347	226	3	1	1	NUM
ejpam-2347	226	4	)	)	PUNCT
ejpam-2347	226	5	.	.	PUNCT
ejpam-2347	227	1	thus	thus	ADV
ejpam-2347	227	2	,	,	PUNCT
ejpam-2347	227	3	using	use	VERB
ejpam-2347	227	4	definition	definition	NOUN
ejpam-2347	227	5	2	2	NUM
ejpam-2347	227	6	we	we	PRON
ejpam-2347	227	7	complete	complete	VERB
ejpam-2347	227	8	the	the	DET
ejpam-2347	227	9	proof	proof	NOUN
ejpam-2347	227	10	of	of	ADP
ejpam-2347	227	11	the	the	DET
ejpam-2347	227	12	theorem	theorem	NOUN
ejpam-2347	227	13	b(n+	b(n+	PROPN
ejpam-2347	227	14	1	1	NUM
ejpam-2347	227	15	,	,	PUNCT
ejpam-2347	227	16	m+	m+	NOUN
ejpam-2347	227	17	1	1	NUM
ejpam-2347	227	18	)	)	PUNCT
ejpam-2347	227	19	=	=	SYM
ejpam-2347	227	20	−bp(n	−bp(n	PROPN
ejpam-2347	227	21	,	,	PUNCT
ejpam-2347	227	22	m	m	NOUN
ejpam-2347	227	23	)	)	PUNCT
ejpam-2347	227	24	�	�	PROPN
ejpam-2347	227	25	n	n	CCONJ
ejpam-2347	227	26	p	p	PROPN
ejpam-2347	227	27	�	�	PROPN
ejpam-2347	227	28	!	!	PUNCT
ejpam-2347	228	1	�	�	PROPN
ejpam-2347	228	2	m	m	PROPN
ejpam-2347	228	3	p	p	PROPN
ejpam-2347	228	4	�	�	PROPN
ejpam-2347	228	5	!	!	PUNCT
ejpam-2347	229	1	�	�	PROPN
ejpam-2347	229	2	m+n	m+n	PROPN
ejpam-2347	229	3	p	p	PROPN
ejpam-2347	229	4	�	�	PROPN
ejpam-2347	229	5	!	!	PUNCT
ejpam-2347	230	1	p	p	PRON
ejpam-2347	230	2	�	�	PROPN
ejpam-2347	230	3	n	n	CCONJ
ejpam-2347	230	4	p	p	PROPN
ejpam-2347	230	5	�	�	PROPN
ejpam-2347	230	6	+	+	CCONJ
ejpam-2347	230	7	�	�	PROPN
ejpam-2347	230	8	m	m	PROPN
ejpam-2347	230	9	p	p	PROPN
ejpam-2347	230	10	�	�	PROPN
ejpam-2347	230	11	−	−	PROPN
ejpam-2347	230	12	�	�	PROPN
ejpam-2347	230	13	m+n	m+n	PROPN
ejpam-2347	231	1	p	p	PROPN
ejpam-2347	232	1	�	�	PROPN
ejpam-2347	233	1	(	(	PUNCT
ejpam-2347	233	2	n+m+	n+m+	X
ejpam-2347	233	3	1	1	NUM
ejpam-2347	233	4	)	)	PUNCT
ejpam-2347	233	5	hp(n)hp(m	hp(n)hp(m	PRON
ejpam-2347	233	6	)	)	PUNCT
ejpam-2347	233	7	hp(n+m	hp(n+m	PROPN
ejpam-2347	233	8	)	)	PUNCT
ejpam-2347	233	9	.	.	PUNCT
ejpam-2347	234	1	theorem	theorem	VERB
ejpam-2347	234	2	9	9	NUM
ejpam-2347	234	3	.	.	PUNCT
ejpam-2347	235	1	the	the	DET
ejpam-2347	235	2	equality	equality	NOUN
ejpam-2347	235	3	b(n+	b(n+	NOUN
ejpam-2347	235	4	1	1	NUM
ejpam-2347	235	5	,	,	PUNCT
ejpam-2347	235	6	m+	m+	NOUN
ejpam-2347	235	7	1	1	NUM
ejpam-2347	235	8	)	)	PUNCT
ejpam-2347	235	9	=	=	SYM
ejpam-2347	235	10	bp(n+	bp(n+	PROPN
ejpam-2347	235	11	1	1	NUM
ejpam-2347	235	12	,	,	PUNCT
ejpam-2347	235	13	m+	m+	NOUN
ejpam-2347	235	14	1	1	NUM
ejpam-2347	235	15	)	)	PUNCT
ejpam-2347	235	16	�	�	PROPN
ejpam-2347	235	17	n	n	CCONJ
ejpam-2347	235	18	p	p	PROPN
ejpam-2347	235	19	�	�	PROPN
ejpam-2347	235	20	!	!	PUNCT
ejpam-2347	236	1	�	�	PROPN
ejpam-2347	236	2	m	m	PROPN
ejpam-2347	236	3	p	p	PROPN
ejpam-2347	236	4	�	�	PROPN
ejpam-2347	236	5	!	!	PUNCT
ejpam-2347	237	1	�	�	PROPN
ejpam-2347	237	2	m+n+1	m+n+1	VERB
ejpam-2347	237	3	p	p	PROPN
ejpam-2347	237	4	�	�	PROPN
ejpam-2347	237	5	!	!	PUNCT
ejpam-2347	238	1	p	p	PRON
ejpam-2347	238	2	�	�	PROPN
ejpam-2347	238	3	n	n	CCONJ
ejpam-2347	238	4	p	p	PROPN
ejpam-2347	238	5	�	�	PROPN
ejpam-2347	238	6	+	+	CCONJ
ejpam-2347	238	7	�	�	PROPN
ejpam-2347	238	8	m	m	PROPN
ejpam-2347	238	9	p	p	PROPN
ejpam-2347	238	10	�	�	PROPN
ejpam-2347	238	11	−	−	PROPN
ejpam-2347	238	12	�	�	PROPN
ejpam-2347	238	13	m+n+1	m+n+1	NOUN
ejpam-2347	238	14	p	p	X
ejpam-2347	238	15	�	�	PROPN
ejpam-2347	238	16	holds	hold	VERB
ejpam-2347	238	17	for	for	ADP
ejpam-2347	238	18	all	all	DET
ejpam-2347	238	19	m	m	NOUN
ejpam-2347	238	20	,	,	PUNCT
ejpam-2347	238	21	n	n	PROPN
ejpam-2347	238	22	∈	∈	PROPN
ejpam-2347	238	23	n.	n.	NOUN
ejpam-2347	238	24	proof	proof	NOUN
ejpam-2347	238	25	.	.	PUNCT
ejpam-2347	239	1	in	in	ADP
ejpam-2347	239	2	similar	similar	ADJ
ejpam-2347	239	3	way	way	NOUN
ejpam-2347	239	4	,	,	PUNCT
ejpam-2347	239	5	using	use	VERB
ejpam-2347	239	6	the	the	DET
ejpam-2347	239	7	definitions	definition	NOUN
ejpam-2347	239	8	and	and	CCONJ
ejpam-2347	239	9	proposition	proposition	NOUN
ejpam-2347	239	10	4(i	4(i	NUM
ejpam-2347	239	11	)	)	PUNCT
ejpam-2347	240	1	we	we	PRON
ejpam-2347	240	2	can	can	AUX
ejpam-2347	240	3	obtain	obtain	VERB
ejpam-2347	240	4	that	that	PRON
ejpam-2347	240	5	b(n+	b(n+	PROPN
ejpam-2347	240	6	1	1	NUM
ejpam-2347	240	7	,	,	PUNCT
ejpam-2347	240	8	m+	m+	NOUN
ejpam-2347	240	9	1	1	NUM
ejpam-2347	240	10	)	)	PUNCT
ejpam-2347	240	11	=	=	PUNCT
ejpam-2347	240	12	γ(n+	γ(n+	NUM
ejpam-2347	241	1	1)γ(m+	1)γ(m+	NUM
ejpam-2347	241	2	1	1	NUM
ejpam-2347	241	3	)	)	PUNCT
ejpam-2347	241	4	γ(n+m+	γ(n+m+	PUNCT
ejpam-2347	242	1	2	2	X
ejpam-2347	242	2	)	)	PUNCT
ejpam-2347	242	3	=	=	SYM
ejpam-2347	243	1	n!m	n!m	PROPN
ejpam-2347	243	2	!	!	PUNCT
ejpam-2347	244	1	(	(	PUNCT
ejpam-2347	244	2	n+m+	n+m+	X
ejpam-2347	244	3	1	1	NUM
ejpam-2347	244	4	)	)	PUNCT
ejpam-2347	244	5	!	!	PUNCT
ejpam-2347	245	1	=	=	PUNCT
ejpam-2347	245	2	(	(	PUNCT
ejpam-2347	245	3	−1)n+1γp(n+	−1)n+1γp(n+	ADP
ejpam-2347	245	4	1	1	NUM
ejpam-2347	245	5	)	)	PUNCT
ejpam-2347	245	6	�	�	PROPN
ejpam-2347	245	7	n	n	CCONJ
ejpam-2347	245	8	p	p	PROPN
ejpam-2347	245	9	�	�	PROPN
ejpam-2347	245	10	!	!	PUNCT
ejpam-2347	246	1	p	p	PROPN
ejpam-2347	246	2	�	�	PROPN
ejpam-2347	246	3	n	n	CCONJ
ejpam-2347	246	4	p	p	PROPN
ejpam-2347	246	5	�	�	PROPN
ejpam-2347	246	6	(	(	PUNCT
ejpam-2347	246	7	−1)m+1γp(m+	−1)m+1γp(m+	PROPN
ejpam-2347	246	8	1	1	NUM
ejpam-2347	246	9	)	)	PUNCT
ejpam-2347	246	10	�	�	PROPN
ejpam-2347	246	11	m	m	PROPN
ejpam-2347	246	12	p	p	NOUN
ejpam-2347	246	13	�	�	PROPN
ejpam-2347	246	14	!	!	PUNCT
ejpam-2347	247	1	p	p	PROPN
ejpam-2347	247	2	�	�	PROPN
ejpam-2347	247	3	m	m	PROPN
ejpam-2347	247	4	p	p	PROPN
ejpam-2347	247	5	�	�	PROPN
ejpam-2347	247	6	(	(	PUNCT
ejpam-2347	247	7	−1)m+n+2γp(m+	−1)m+n+2γp(m+	X
ejpam-2347	247	8	n+	n+	NOUN
ejpam-2347	247	9	2	2	NUM
ejpam-2347	247	10	)	)	PUNCT
ejpam-2347	247	11	�	�	PROPN
ejpam-2347	247	12	m+n+1	m+n+1	VERB
ejpam-2347	247	13	p	p	PROPN
ejpam-2347	247	14	�	�	PROPN
ejpam-2347	247	15	!	!	PUNCT
ejpam-2347	248	1	p	p	PRON
ejpam-2347	248	2	�	�	PROPN
ejpam-2347	248	3	m+n+1	m+n+1	VERB
ejpam-2347	248	4	p	p	PROPN
ejpam-2347	248	5	�	�	PROPN
ejpam-2347	248	6	h.	h.	PROPN
ejpam-2347	248	7	menken	menken	PROPN
ejpam-2347	248	8	,	,	PUNCT
ejpam-2347	248	9	ö.	ö.	VERB
ejpam-2347	248	10	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	248	11	/	/	SYM
ejpam-2347	248	12	eur	eur	PROPN
ejpam-2347	248	13	.	.	PUNCT
ejpam-2347	249	1	j.	j.	PROPN
ejpam-2347	249	2	pure	pure	PROPN
ejpam-2347	249	3	appl	appl	PROPN
ejpam-2347	249	4	.	.	PROPN
ejpam-2347	249	5	math	math	PROPN
ejpam-2347	249	6	,	,	PUNCT
ejpam-2347	249	7	8	8	NUM
ejpam-2347	249	8	(	(	PUNCT
ejpam-2347	249	9	2015	2015	NUM
ejpam-2347	249	10	)	)	PUNCT
ejpam-2347	249	11	,	,	PUNCT
ejpam-2347	249	12	214	214	NUM
ejpam-2347	249	13	-	-	SYM
ejpam-2347	249	14	231	231	NUM
ejpam-2347	249	15	225	225	NUM
ejpam-2347	249	16	=	=	SYM
ejpam-2347	249	17	γp(n+	γp(n+	ADP
ejpam-2347	249	18	1)γp(m+	1)γp(m+	NOUN
ejpam-2347	249	19	1	1	NUM
ejpam-2347	249	20	)	)	PUNCT
ejpam-2347	249	21	γp(m+	γp(m+	NOUN
ejpam-2347	249	22	n+	n+	PUNCT
ejpam-2347	249	23	2	2	NUM
ejpam-2347	249	24	)	)	PUNCT
ejpam-2347	249	25	�	�	PROPN
ejpam-2347	249	26	n	n	CCONJ
ejpam-2347	249	27	p	p	PROPN
ejpam-2347	249	28	�	�	PROPN
ejpam-2347	249	29	!	!	PUNCT
ejpam-2347	250	1	�	�	PROPN
ejpam-2347	250	2	m	m	PROPN
ejpam-2347	250	3	p	p	PROPN
ejpam-2347	250	4	�	�	PROPN
ejpam-2347	250	5	!	!	PUNCT
ejpam-2347	251	1	�	�	PROPN
ejpam-2347	251	2	m+n+1	m+n+1	VERB
ejpam-2347	251	3	p	p	PROPN
ejpam-2347	251	4	�	�	PROPN
ejpam-2347	251	5	!	!	PUNCT
ejpam-2347	252	1	p	p	PRON
ejpam-2347	252	2	�	�	PROPN
ejpam-2347	252	3	n	n	CCONJ
ejpam-2347	252	4	p	p	PROPN
ejpam-2347	252	5	�	�	PROPN
ejpam-2347	252	6	+	+	CCONJ
ejpam-2347	252	7	�	�	PROPN
ejpam-2347	252	8	m	m	PROPN
ejpam-2347	252	9	p	p	PROPN
ejpam-2347	252	10	�	�	PROPN
ejpam-2347	252	11	−[m+n+1	−[m+n+1	PROPN
ejpam-2347	252	12	p	p	X
ejpam-2347	252	13	]	]	X
ejpam-2347	252	14	=	=	X
ejpam-2347	252	15	bp(n+	bp(n+	PROPN
ejpam-2347	252	16	1	1	NUM
ejpam-2347	252	17	,	,	PUNCT
ejpam-2347	252	18	m+	m+	NOUN
ejpam-2347	252	19	1	1	NUM
ejpam-2347	252	20	)	)	PUNCT
ejpam-2347	252	21	�	�	PROPN
ejpam-2347	252	22	n	n	CCONJ
ejpam-2347	252	23	p	p	PROPN
ejpam-2347	252	24	�	�	PROPN
ejpam-2347	252	25	!	!	PUNCT
ejpam-2347	253	1	�	�	PROPN
ejpam-2347	253	2	m	m	PROPN
ejpam-2347	253	3	p	p	PROPN
ejpam-2347	253	4	�	�	PROPN
ejpam-2347	253	5	!	!	PUNCT
ejpam-2347	254	1	�	�	PROPN
ejpam-2347	254	2	m+n+1	m+n+1	VERB
ejpam-2347	254	3	p	p	PROPN
ejpam-2347	254	4	�	�	PROPN
ejpam-2347	254	5	!	!	PUNCT
ejpam-2347	255	1	p	p	PRON
ejpam-2347	255	2	�	�	PROPN
ejpam-2347	255	3	n	n	CCONJ
ejpam-2347	255	4	p	p	PROPN
ejpam-2347	255	5	�	�	PROPN
ejpam-2347	255	6	+	+	CCONJ
ejpam-2347	255	7	�	�	PROPN
ejpam-2347	255	8	m	m	PROPN
ejpam-2347	255	9	p	p	PROPN
ejpam-2347	255	10	�	�	PROPN
ejpam-2347	255	11	−[m+n+1	−[m+n+1	PROPN
ejpam-2347	255	12	p	p	X
ejpam-2347	255	13	]	]	PUNCT
ejpam-2347	255	14	.	.	PUNCT
ejpam-2347	256	1	theorem	theorem	ADJ
ejpam-2347	256	2	10	10	NUM
ejpam-2347	256	3	.	.	PUNCT
ejpam-2347	257	1	the	the	DET
ejpam-2347	257	2	equality	equality	NOUN
ejpam-2347	257	3	b(pn	b(pn	PROPN
ejpam-2347	257	4	+	+	CCONJ
ejpam-2347	257	5	1	1	NUM
ejpam-2347	257	6	,	,	PUNCT
ejpam-2347	257	7	pm	pm	NOUN
ejpam-2347	257	8	+	+	NOUN
ejpam-2347	257	9	1	1	X
ejpam-2347	257	10	)	)	PUNCT
ejpam-2347	257	11	=	=	SYM
ejpam-2347	257	12	bp(p	bp(p	NOUN
ejpam-2347	257	13	n	n	CCONJ
ejpam-2347	257	14	,	,	PUNCT
ejpam-2347	257	15	pm	pm	NOUN
ejpam-2347	257	16	)	)	PUNCT
ejpam-2347	257	17	(	(	PUNCT
ejpam-2347	257	18	pn−1)!(pm−1	pn−1)!(pm−1	PROPN
ejpam-2347	257	19	)	)	PUNCT
ejpam-2347	257	20	!	!	PUNCT
ejpam-2347	258	1	(	(	PUNCT
ejpam-2347	258	2	pn−1	pn−1	PROPN
ejpam-2347	258	3	+	+	CCONJ
ejpam-2347	258	4	pm−1	pm−1	NOUN
ejpam-2347	258	5	)	)	PUNCT
ejpam-2347	258	6	!	!	PUNCT
ejpam-2347	259	1	1	1	NUM
ejpam-2347	259	2	hp(p	hp(p	NUM
ejpam-2347	259	3	n	n	PRON
ejpam-2347	259	4	+	+	NOUN
ejpam-2347	259	5	pm)(pn	pm)(pn	PROPN
ejpam-2347	259	6	+	+	NUM
ejpam-2347	259	7	pm	pm	NOUN
ejpam-2347	259	8	+	+	NOUN
ejpam-2347	259	9	1	1	X
ejpam-2347	259	10	)	)	PUNCT
ejpam-2347	259	11	holds	hold	VERB
ejpam-2347	259	12	for	for	ADP
ejpam-2347	259	13	all	all	DET
ejpam-2347	259	14	m	m	NOUN
ejpam-2347	259	15	,	,	PUNCT
ejpam-2347	259	16	n	n	PROPN
ejpam-2347	259	17	∈	∈	PROPN
ejpam-2347	259	18	n.	n.	NOUN
ejpam-2347	259	19	proof	proof	NOUN
ejpam-2347	259	20	.	.	PUNCT
ejpam-2347	260	1	from	from	ADP
ejpam-2347	260	2	the	the	DET
ejpam-2347	260	3	definition	definition	NOUN
ejpam-2347	260	4	of	of	ADP
ejpam-2347	260	5	classical	classical	ADJ
ejpam-2347	260	6	beta	beta	NOUN
ejpam-2347	260	7	function	function	NOUN
ejpam-2347	260	8	and	and	CCONJ
ejpam-2347	260	9	main	main	ADJ
ejpam-2347	260	10	proposition	proposition	NOUN
ejpam-2347	260	11	of	of	ADP
ejpam-2347	260	12	classical	classical	ADJ
ejpam-2347	260	13	gamma	gamma	NOUN
ejpam-2347	260	14	function	function	NOUN
ejpam-2347	260	15	follow	follow	VERB
ejpam-2347	260	16	that	that	SCONJ
ejpam-2347	260	17	b(pn	b(pn	NOUN
ejpam-2347	260	18	+	+	CCONJ
ejpam-2347	260	19	1	1	NUM
ejpam-2347	260	20	,	,	PUNCT
ejpam-2347	260	21	pm	pm	NOUN
ejpam-2347	260	22	+	+	NOUN
ejpam-2347	260	23	1	1	X
ejpam-2347	260	24	)	)	PUNCT
ejpam-2347	260	25	=	=	PUNCT
ejpam-2347	261	1	γ(pn	γ(pn	NOUN
ejpam-2347	261	2	+	+	NOUN
ejpam-2347	261	3	1)γ(pm	1)γ(pm	NUM
ejpam-2347	261	4	+	+	CCONJ
ejpam-2347	261	5	1	1	NUM
ejpam-2347	261	6	)	)	PUNCT
ejpam-2347	261	7	γ(pn	γ(pn	NOUN
ejpam-2347	261	8	+	+	CCONJ
ejpam-2347	261	9	pm	pm	NOUN
ejpam-2347	261	10	+	+	CCONJ
ejpam-2347	261	11	2	2	NUM
ejpam-2347	261	12	)	)	PUNCT
ejpam-2347	261	13	=	=	SYM
ejpam-2347	262	1	pn!pm	pn!pm	PROPN
ejpam-2347	262	2	!	!	PUNCT
ejpam-2347	263	1	(	(	PUNCT
ejpam-2347	263	2	pn	pn	NOUN
ejpam-2347	263	3	+	+	CCONJ
ejpam-2347	263	4	pm	pm	NOUN
ejpam-2347	263	5	+	+	CCONJ
ejpam-2347	263	6	1)(pn	1)(pn	NUM
ejpam-2347	263	7	+	+	CCONJ
ejpam-2347	263	8	pm	pm	NOUN
ejpam-2347	263	9	)	)	PUNCT
ejpam-2347	263	10	!	!	PUNCT
ejpam-2347	264	1	by	by	ADP
ejpam-2347	264	2	proposition	proposition	NOUN
ejpam-2347	264	3	4	4	NUM
ejpam-2347	264	4	(	(	PUNCT
ejpam-2347	264	5	i	i	NOUN
ejpam-2347	264	6	)	)	PUNCT
ejpam-2347	264	7	and	and	CCONJ
ejpam-2347	264	8	(	(	PUNCT
ejpam-2347	264	9	ii	ii	NOUN
ejpam-2347	264	10	)	)	PUNCT
ejpam-2347	264	11	we	we	PRON
ejpam-2347	264	12	get	get	VERB
ejpam-2347	264	13	b(pn	b(pn	NOUN
ejpam-2347	264	14	+	+	CCONJ
ejpam-2347	264	15	1	1	NUM
ejpam-2347	264	16	,	,	PUNCT
ejpam-2347	264	17	pm	pm	NOUN
ejpam-2347	265	1	+	+	NOUN
ejpam-2347	265	2	1	1	X
ejpam-2347	265	3	)	)	PUNCT
ejpam-2347	265	4	=	=	SYM
ejpam-2347	266	1	γp(p	γp(p	NUM
ejpam-2347	266	2	n)(−1)p(pn−1)!ppn−1	n)(−1)p(pn−1)!ppn−1	PROPN
ejpam-2347	266	3	γp(p	γp(p	NOUN
ejpam-2347	266	4	m)(−1)p(pm−1)!ppm−1	m)(−1)p(pm−1)!ppm−1	PROPN
ejpam-2347	266	5	(	(	PUNCT
ejpam-2347	266	6	pn	pn	NOUN
ejpam-2347	266	7	+	+	CCONJ
ejpam-2347	266	8	pm	pm	NOUN
ejpam-2347	266	9	+	+	CCONJ
ejpam-2347	266	10	1)γp(p	1)γp(p	NUM
ejpam-2347	266	11	n	n	NOUN
ejpam-2347	266	12	+	+	CCONJ
ejpam-2347	266	13	pm	pm	NOUN
ejpam-2347	266	14	+	+	CCONJ
ejpam-2347	266	15	1)(−1)pn+pm	1)(−1)pn+pm	NUM
ejpam-2347	266	16	�	�	PROPN
ejpam-2347	266	17	pn+pm	pn+pm	VERB
ejpam-2347	266	18	p	p	PROPN
ejpam-2347	266	19	�	�	PROPN
ejpam-2347	266	20	!	!	PUNCT
ejpam-2347	267	1	p	p	PROPN
ejpam-2347	267	2	�	�	PROPN
ejpam-2347	267	3	pn+pm	pn+pm	PROPN
ejpam-2347	267	4	p	p	PROPN
ejpam-2347	267	5	�	�	PROPN
ejpam-2347	267	6	hence	hence	ADV
ejpam-2347	267	7	,	,	PUNCT
ejpam-2347	267	8	we	we	PRON
ejpam-2347	267	9	obtain	obtain	VERB
ejpam-2347	267	10	b(pn	b(pn	NOUN
ejpam-2347	267	11	+	+	CCONJ
ejpam-2347	267	12	1	1	NUM
ejpam-2347	267	13	,	,	PUNCT
ejpam-2347	267	14	pm	pm	NOUN
ejpam-2347	267	15	+	+	NOUN
ejpam-2347	267	16	1	1	X
ejpam-2347	267	17	)	)	PUNCT
ejpam-2347	267	18	=	=	PUNCT
ejpam-2347	267	19	γp(p	γp(p	VERB
ejpam-2347	267	20	n)γp(p	n)γp(p	NUM
ejpam-2347	267	21	m	m	NOUN
ejpam-2347	267	22	)	)	PUNCT
ejpam-2347	267	23	γp(p	γp(p	PART
ejpam-2347	268	1	n	n	PROPN
ejpam-2347	268	2	+	+	CCONJ
ejpam-2347	268	3	pm	pm	NOUN
ejpam-2347	268	4	)	)	PUNCT
ejpam-2347	268	5	(	(	PUNCT
ejpam-2347	268	6	pn−1)!(pm−1)!ppn−1	pn−1)!(pm−1)!ppn−1	PROPN
ejpam-2347	268	7	ppm−1	ppm−1	PROPN
ejpam-2347	268	8	hp(p	hp(p	X
ejpam-2347	268	9	n	n	PROPN
ejpam-2347	268	10	+	+	CCONJ
ejpam-2347	268	11	pm)(pn−1	pm)(pn−1	PROPN
ejpam-2347	268	12	+	+	CCONJ
ejpam-2347	268	13	pm−1)!ppn−1+pm−1	pm−1)!ppn−1+pm−1	NOUN
ejpam-2347	268	14	(	(	PUNCT
ejpam-2347	268	15	pn	pn	NOUN
ejpam-2347	268	16	+	+	CCONJ
ejpam-2347	268	17	pm	pm	NOUN
ejpam-2347	268	18	+	+	CCONJ
ejpam-2347	268	19	1	1	X
ejpam-2347	268	20	)	)	PUNCT
ejpam-2347	268	21	=	=	NOUN
ejpam-2347	268	22	bp(p	bp(p	X
ejpam-2347	268	23	n	n	NOUN
ejpam-2347	268	24	,	,	PUNCT
ejpam-2347	268	25	pm	pm	NOUN
ejpam-2347	268	26	)	)	PUNCT
ejpam-2347	268	27	(	(	PUNCT
ejpam-2347	268	28	pn−1)!(pm−1	pn−1)!(pm−1	PROPN
ejpam-2347	268	29	)	)	PUNCT
ejpam-2347	268	30	!	!	PUNCT
ejpam-2347	269	1	(	(	PUNCT
ejpam-2347	269	2	pn−1	pn−1	PROPN
ejpam-2347	269	3	+	+	CCONJ
ejpam-2347	269	4	pm−1	pm−1	NOUN
ejpam-2347	269	5	)	)	PUNCT
ejpam-2347	269	6	!	!	PUNCT
ejpam-2347	270	1	1	1	NUM
ejpam-2347	270	2	hp(p	hp(p	NUM
ejpam-2347	270	3	n	n	PRON
ejpam-2347	270	4	+	+	NOUN
ejpam-2347	270	5	pm)(pn	pm)(pn	PROPN
ejpam-2347	270	6	+	+	NUM
ejpam-2347	270	7	pm	pm	NOUN
ejpam-2347	270	8	+	+	NOUN
ejpam-2347	270	9	1	1	NUM
ejpam-2347	270	10	)	)	PUNCT
ejpam-2347	270	11	.	.	PUNCT
ejpam-2347	271	1	corollary	corollary	ADJ
ejpam-2347	271	2	6	6	NUM
ejpam-2347	271	3	.	.	PUNCT
ejpam-2347	272	1	if	if	SCONJ
ejpam-2347	272	2	p	p	PROPN
ejpam-2347	272	3	6=	6=	NUM
ejpam-2347	272	4	2	2	NUM
ejpam-2347	272	5	then	then	ADV
ejpam-2347	272	6	bp	bp	PROPN
ejpam-2347	272	7	(	(	PUNCT
ejpam-2347	272	8	1	1	NUM
ejpam-2347	272	9	2	2	NUM
ejpam-2347	272	10	,	,	PUNCT
ejpam-2347	272	11	1	1	NUM
ejpam-2347	272	12	2	2	NUM
ejpam-2347	272	13	)	)	PUNCT
ejpam-2347	272	14	=	=	PUNCT
ejpam-2347	272	15	¨	¨	NOUN
ejpam-2347	272	16	−1	−1	NOUN
ejpam-2347	272	17	if	if	SCONJ
ejpam-2347	272	18	p	p	PRON
ejpam-2347	272	19	≡	≡	PROPN
ejpam-2347	272	20	3	3	NUM
ejpam-2347	272	21	(	(	PUNCT
ejpam-2347	272	22	mod	mod	NOUN
ejpam-2347	272	23	4	4	NUM
ejpam-2347	272	24	)	)	PUNCT
ejpam-2347	272	25	1	1	NUM
ejpam-2347	272	26	if	if	SCONJ
ejpam-2347	272	27	p	p	PRON
ejpam-2347	272	28	≡	≡	PROPN
ejpam-2347	272	29	1	1	NUM
ejpam-2347	272	30	(	(	PUNCT
ejpam-2347	272	31	mod	mod	NOUN
ejpam-2347	272	32	4	4	NUM
ejpam-2347	272	33	)	)	PUNCT
ejpam-2347	272	34	proof	proof	NOUN
ejpam-2347	272	35	.	.	PUNCT
ejpam-2347	273	1	using	use	VERB
ejpam-2347	273	2	corollary	corollary	ADJ
ejpam-2347	273	3	2	2	NUM
ejpam-2347	273	4	and	and	CCONJ
ejpam-2347	273	5	proposition	proposition	NOUN
ejpam-2347	273	6	1	1	NUM
ejpam-2347	273	7	,	,	PUNCT
ejpam-2347	273	8	we	we	PRON
ejpam-2347	273	9	have	have	VERB
ejpam-2347	273	10	bp	bp	PROPN
ejpam-2347	273	11	(	(	PUNCT
ejpam-2347	273	12	1	1	NUM
ejpam-2347	273	13	2	2	NUM
ejpam-2347	273	14	,	,	PUNCT
ejpam-2347	273	15	1	1	NUM
ejpam-2347	273	16	2	2	NUM
ejpam-2347	273	17	)	)	PUNCT
ejpam-2347	274	1	=	=	SYM
ejpam-2347	274	2	γp	γp	PROPN
ejpam-2347	274	3	(	(	PUNCT
ejpam-2347	274	4	1	1	NUM
ejpam-2347	274	5	2)γp	2)γp	PROPN
ejpam-2347	274	6	(	(	PUNCT
ejpam-2347	274	7	1	1	NUM
ejpam-2347	274	8	2	2	NUM
ejpam-2347	274	9	)	)	PUNCT
ejpam-2347	274	10	γp(1	γp(1	PROPN
ejpam-2347	274	11	)	)	PUNCT
ejpam-2347	274	12	h.	h.	PROPN
ejpam-2347	274	13	menken	menken	PROPN
ejpam-2347	274	14	,	,	PUNCT
ejpam-2347	274	15	ö.	ö.	VERB
ejpam-2347	274	16	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	274	17	/	/	SYM
ejpam-2347	274	18	eur	eur	PROPN
ejpam-2347	274	19	.	.	PUNCT
ejpam-2347	275	1	j.	j.	PROPN
ejpam-2347	275	2	pure	pure	PROPN
ejpam-2347	275	3	appl	appl	PROPN
ejpam-2347	275	4	.	.	PROPN
ejpam-2347	275	5	math	math	PROPN
ejpam-2347	275	6	,	,	PUNCT
ejpam-2347	275	7	8	8	NUM
ejpam-2347	275	8	(	(	PUNCT
ejpam-2347	275	9	2015	2015	NUM
ejpam-2347	275	10	)	)	PUNCT
ejpam-2347	275	11	,	,	PUNCT
ejpam-2347	275	12	214	214	NUM
ejpam-2347	275	13	-	-	SYM
ejpam-2347	275	14	231	231	NUM
ejpam-2347	275	15	226	226	NUM
ejpam-2347	275	16	=(	=(	NOUN
ejpam-2347	275	17	−1)ℓ	−1)ℓ	NOUN
ejpam-2347	275	18	(	(	PUNCT
ejpam-2347	275	19	1	1	NUM
ejpam-2347	275	20	2	2	NUM
ejpam-2347	275	21	)	)	PUNCT
ejpam-2347	275	22	+1	+1	PROPN
ejpam-2347	275	23	,	,	PUNCT
ejpam-2347	275	24	ℓ	ℓ	INTJ
ejpam-2347	275	25	(	(	PUNCT
ejpam-2347	275	26	1	1	NUM
ejpam-2347	275	27	2	2	NUM
ejpam-2347	275	28	)	)	PUNCT
ejpam-2347	275	29	=	=	SYM
ejpam-2347	275	30	ℓ	ℓ	X
ejpam-2347	275	31	(	(	PUNCT
ejpam-2347	275	32	1	1	NUM
ejpam-2347	275	33	2	2	NUM
ejpam-2347	275	34	(	(	PUNCT
ejpam-2347	275	35	p+	p+	NOUN
ejpam-2347	275	36	1	1	NUM
ejpam-2347	275	37	)	)	PUNCT
ejpam-2347	275	38	)	)	PUNCT
ejpam-2347	276	1	=	=	SYM
ejpam-2347	276	2	1	1	NUM
ejpam-2347	276	3	2	2	NUM
ejpam-2347	276	4	(	(	PUNCT
ejpam-2347	276	5	p+	p+	NOUN
ejpam-2347	276	6	1	1	NUM
ejpam-2347	276	7	)	)	PUNCT
ejpam-2347	276	8	=(	=(	NOUN
ejpam-2347	276	9	−1	−1	NOUN
ejpam-2347	276	10	)	)	PUNCT
ejpam-2347	276	11	.	.	PUNCT
ejpam-2347	277	1	¨	¨	NOUN
ejpam-2347	277	2	1	1	NUM
ejpam-2347	277	3	if	if	SCONJ
ejpam-2347	277	4	p	p	PRON
ejpam-2347	277	5	≡	≡	PROPN
ejpam-2347	277	6	3	3	NUM
ejpam-2347	277	7	(	(	PUNCT
ejpam-2347	277	8	mod	mod	NOUN
ejpam-2347	277	9	4	4	NUM
ejpam-2347	277	10	)	)	PUNCT
ejpam-2347	277	11	−1	−1	NOUN
ejpam-2347	277	12	if	if	SCONJ
ejpam-2347	277	13	p	p	PRON
ejpam-2347	277	14	≡	≡	PROPN
ejpam-2347	277	15	1	1	NUM
ejpam-2347	277	16	(	(	PUNCT
ejpam-2347	277	17	mod	mod	NOUN
ejpam-2347	277	18	4	4	NUM
ejpam-2347	277	19	)	)	PUNCT
ejpam-2347	277	20	=	=	PUNCT
ejpam-2347	277	21	¨	¨	NOUN
ejpam-2347	277	22	−1	−1	NOUN
ejpam-2347	277	23	if	if	SCONJ
ejpam-2347	277	24	p	p	PRON
ejpam-2347	277	25	≡	≡	PROPN
ejpam-2347	277	26	3	3	NUM
ejpam-2347	277	27	(	(	PUNCT
ejpam-2347	277	28	mod	mod	NOUN
ejpam-2347	277	29	4	4	NUM
ejpam-2347	277	30	)	)	PUNCT
ejpam-2347	277	31	1	1	NUM
ejpam-2347	277	32	if	if	SCONJ
ejpam-2347	277	33	p	p	PRON
ejpam-2347	277	34	≡	≡	PROPN
ejpam-2347	277	35	1	1	NUM
ejpam-2347	277	36	(	(	PUNCT
ejpam-2347	277	37	mod	mod	NOUN
ejpam-2347	277	38	4	4	NUM
ejpam-2347	277	39	)	)	PUNCT
ejpam-2347	277	40	.	.	PUNCT
ejpam-2347	278	1	now	now	ADV
ejpam-2347	278	2	we	we	PRON
ejpam-2347	278	3	prove	prove	VERB
ejpam-2347	278	4	that	that	SCONJ
ejpam-2347	278	5	the	the	DET
ejpam-2347	278	6	p	p	NOUN
ejpam-2347	278	7	-	-	PUNCT
ejpam-2347	278	8	adic	adic	ADJ
ejpam-2347	278	9	beta	beta	NOUN
ejpam-2347	278	10	function	function	NOUN
ejpam-2347	278	11	has	have	VERB
ejpam-2347	278	12	the	the	DET
ejpam-2347	278	13	following	follow	VERB
ejpam-2347	278	14	properties	property	NOUN
ejpam-2347	278	15	for	for	ADP
ejpam-2347	278	16	negative	negative	ADJ
ejpam-2347	278	17	integers	integer	NOUN
ejpam-2347	278	18	.	.	PUNCT
ejpam-2347	279	1	theorem	theorem	VERB
ejpam-2347	279	2	11	11	NUM
ejpam-2347	279	3	.	.	PUNCT
ejpam-2347	280	1	if	if	SCONJ
ejpam-2347	280	2	n	n	CCONJ
ejpam-2347	280	3	,	,	PUNCT
ejpam-2347	280	4	m	m	VERB
ejpam-2347	280	5	∈	∈	PROPN
ejpam-2347	280	6	n	n	CCONJ
ejpam-2347	280	7	,	,	PUNCT
ejpam-2347	280	8	then	then	ADV
ejpam-2347	280	9	bp(−n,−m	bp(−n,−m	PROPN
ejpam-2347	280	10	)	)	PUNCT
ejpam-2347	281	1	=	=	SYM
ejpam-2347	281	2	(	(	PUNCT
ejpam-2347	281	3	−1	−1	NOUN
ejpam-2347	281	4	)	)	PUNCT
ejpam-2347	281	5	�	�	PROPN
ejpam-2347	281	6	1	1	NUM
ejpam-2347	281	7	+	+	NUM
ejpam-2347	281	8	�	�	PROPN
ejpam-2347	281	9	n+m	n+m	NUM
ejpam-2347	281	10	p	p	PROPN
ejpam-2347	281	11	�	�	PROPN
ejpam-2347	281	12	−	−	PROPN
ejpam-2347	281	13	�	�	PROPN
ejpam-2347	281	14	n	n	CCONJ
ejpam-2347	281	15	p	p	PROPN
ejpam-2347	281	16	�	�	PROPN
ejpam-2347	281	17	−	−	PROPN
ejpam-2347	281	18	�	�	PROPN
ejpam-2347	281	19	m	m	PROPN
ejpam-2347	281	20	p	p	PROPN
ejpam-2347	281	21	�	�	PROPN
ejpam-2347	281	22	�	�	PROPN
ejpam-2347	281	23	hp(n+m	hp(n+m	PROPN
ejpam-2347	281	24	)	)	PUNCT
ejpam-2347	281	25	hp(n)hp(m	hp(n)hp(m	X
ejpam-2347	281	26	)	)	PUNCT
ejpam-2347	281	27	1	1	NUM
ejpam-2347	281	28	bp(n	bp(n	X
ejpam-2347	281	29	,	,	PUNCT
ejpam-2347	281	30	m	m	NOUN
ejpam-2347	281	31	)	)	PUNCT
ejpam-2347	281	32	proof	proof	NOUN
ejpam-2347	281	33	.	.	PUNCT
ejpam-2347	282	1	by	by	ADP
ejpam-2347	282	2	definition	definition	NOUN
ejpam-2347	282	3	2	2	NUM
ejpam-2347	282	4	and	and	CCONJ
ejpam-2347	282	5	proposition	proposition	NOUN
ejpam-2347	282	6	2	2	NUM
ejpam-2347	282	7	we	we	PRON
ejpam-2347	282	8	get	get	VERB
ejpam-2347	282	9	bp(−n,−m	bp(−n,−m	NOUN
ejpam-2347	282	10	)	)	PUNCT
ejpam-2347	282	11	=	=	PUNCT
ejpam-2347	282	12	γp(−n)γp(−m	γp(−n)γp(−m	X
ejpam-2347	282	13	)	)	PUNCT
ejpam-2347	282	14	γp(−n−m	γp(−n−m	NOUN
ejpam-2347	282	15	)	)	PUNCT
ejpam-2347	283	1	=	=	SYM
ejpam-2347	284	1	(	(	PUNCT
ejpam-2347	284	2	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	284	3	�	�	PROPN
ejpam-2347	284	4	n	n	CCONJ
ejpam-2347	284	5	p	p	PROPN
ejpam-2347	284	6	�	�	PROPN
ejpam-2347	284	7	(	(	PUNCT
ejpam-2347	284	8	γp(n+	γp(n+	PROPN
ejpam-2347	284	9	1))−1(−1)m+1−	1))−1(−1)m+1−	NUM
ejpam-2347	284	10	�	�	PROPN
ejpam-2347	284	11	m	m	PROPN
ejpam-2347	284	12	p	p	PROPN
ejpam-2347	284	13	�	�	PROPN
ejpam-2347	284	14	(	(	PUNCT
ejpam-2347	284	15	γp(m+	γp(m+	NOUN
ejpam-2347	284	16	1))−1	1))−1	NUM
ejpam-2347	284	17	(	(	PUNCT
ejpam-2347	284	18	−1)n+m+1−	−1)n+m+1−	PROPN
ejpam-2347	284	19	�	�	PROPN
ejpam-2347	284	20	n+m	n+m	NUM
ejpam-2347	284	21	p	p	PROPN
ejpam-2347	284	22	�	�	PROPN
ejpam-2347	284	23	(	(	PUNCT
ejpam-2347	284	24	γp(n+m+	γp(n+m+	PROPN
ejpam-2347	284	25	1))−1	1))−1	NUM
ejpam-2347	284	26	,	,	PUNCT
ejpam-2347	284	27	and	and	CCONJ
ejpam-2347	284	28	by	by	ADP
ejpam-2347	284	29	proposition	proposition	NOUN
ejpam-2347	284	30	1(i	1(i	NUM
ejpam-2347	284	31	)	)	PUNCT
ejpam-2347	284	32	we	we	PRON
ejpam-2347	284	33	have	have	VERB
ejpam-2347	284	34	bp(−n,−m	bp(−n,−m	NOUN
ejpam-2347	284	35	)	)	PUNCT
ejpam-2347	284	36	=(	=(	NOUN
ejpam-2347	284	37	−1)1	−1)1	NUM
ejpam-2347	285	1	+	+	X
ejpam-2347	286	1	�	�	PROPN
ejpam-2347	287	1	n+m	n+m	NUM
ejpam-2347	287	2	p	p	PROPN
ejpam-2347	287	3	�	�	PROPN
ejpam-2347	287	4	−	−	PROPN
ejpam-2347	287	5	�	�	PROPN
ejpam-2347	287	6	n	n	CCONJ
ejpam-2347	287	7	p	p	PROPN
ejpam-2347	287	8	�	�	PROPN
ejpam-2347	287	9	−	−	PROPN
ejpam-2347	287	10	�	�	PROPN
ejpam-2347	287	11	m	m	PROPN
ejpam-2347	287	12	p	p	NOUN
ejpam-2347	287	13	�	�	PROPN
ejpam-2347	287	14	γp(n+m+	γp(n+m+	ADP
ejpam-2347	287	15	1	1	NUM
ejpam-2347	287	16	)	)	PUNCT
ejpam-2347	287	17	γp(n+	γp(n+	ADP
ejpam-2347	287	18	1)γp(m+	1)γp(m+	NOUN
ejpam-2347	287	19	1	1	NUM
ejpam-2347	287	20	)	)	PUNCT
ejpam-2347	287	21	=(	=(	NOUN
ejpam-2347	288	1	−1)1	−1)1	NUM
ejpam-2347	288	2	+	+	X
ejpam-2347	288	3	�	�	PROPN
ejpam-2347	288	4	n+m	n+m	NUM
ejpam-2347	288	5	p	p	PROPN
ejpam-2347	288	6	�	�	PROPN
ejpam-2347	288	7	−	−	PROPN
ejpam-2347	288	8	�	�	PROPN
ejpam-2347	288	9	n	n	CCONJ
ejpam-2347	288	10	p	p	PROPN
ejpam-2347	288	11	�	�	PROPN
ejpam-2347	288	12	−	−	PROPN
ejpam-2347	288	13	�	�	PROPN
ejpam-2347	288	14	m	m	PROPN
ejpam-2347	288	15	p	p	PROPN
ejpam-2347	288	16	�	�	PROPN
ejpam-2347	288	17	γp(n+m)hp(n+m	γp(n+m)hp(n+m	PROPN
ejpam-2347	288	18	)	)	PUNCT
ejpam-2347	288	19	γp(n)hp(n)γp(m)hp(m	γp(n)hp(n)γp(m)hp(m	PROPN
ejpam-2347	288	20	)	)	PUNCT
ejpam-2347	288	21	=(	=(	NOUN
ejpam-2347	288	22	−1)1	−1)1	NUM
ejpam-2347	288	23	+	+	X
ejpam-2347	288	24	�	�	PROPN
ejpam-2347	288	25	n+m	n+m	NUM
ejpam-2347	288	26	p	p	PROPN
ejpam-2347	288	27	�	�	PROPN
ejpam-2347	288	28	−	−	PROPN
ejpam-2347	288	29	�	�	PROPN
ejpam-2347	288	30	n	n	CCONJ
ejpam-2347	288	31	p	p	PROPN
ejpam-2347	288	32	�	�	PROPN
ejpam-2347	288	33	−	−	PROPN
ejpam-2347	288	34	�	�	PROPN
ejpam-2347	288	35	m	m	PROPN
ejpam-2347	288	36	p	p	PROPN
ejpam-2347	288	37	�	�	PROPN
ejpam-2347	288	38	hp(n+m	hp(n+m	PROPN
ejpam-2347	288	39	)	)	PUNCT
ejpam-2347	288	40	hp(n)hp(m	hp(n)hp(m	X
ejpam-2347	288	41	)	)	PUNCT
ejpam-2347	288	42	1	1	NUM
ejpam-2347	288	43	bp(n	bp(n	NOUN
ejpam-2347	288	44	,	,	PUNCT
ejpam-2347	288	45	m	m	NOUN
ejpam-2347	288	46	)	)	PUNCT
ejpam-2347	288	47	.	.	PUNCT
ejpam-2347	289	1	theorem	theorem	NOUN
ejpam-2347	289	2	12	12	NUM
ejpam-2347	289	3	.	.	PUNCT
ejpam-2347	290	1	if	if	SCONJ
ejpam-2347	290	2	n	n	CCONJ
ejpam-2347	290	3	,	,	PUNCT
ejpam-2347	290	4	m	m	VERB
ejpam-2347	290	5	∈	∈	PROPN
ejpam-2347	290	6	n	n	CCONJ
ejpam-2347	290	7	,	,	PUNCT
ejpam-2347	290	8	then	then	ADV
ejpam-2347	290	9	bp(−n	bp(−n	ADJ
ejpam-2347	290	10	,	,	PUNCT
ejpam-2347	290	11	m	m	NOUN
ejpam-2347	290	12	)	)	PUNCT
ejpam-2347	291	1	=	=	PUNCT
ejpam-2347	291	2			PROPN
ejpam-2347	291	3			PROPN
ejpam-2347	291	4			PROPN
ejpam-2347	291	5	(	(	PUNCT
ejpam-2347	291	6	−1)m−	−1)m−	X
ejpam-2347	291	7	�	�	PROPN
ejpam-2347	291	8	n	n	CCONJ
ejpam-2347	291	9	p	p	PROPN
ejpam-2347	291	10	�	�	PROPN
ejpam-2347	291	11	+	+	CCONJ
ejpam-2347	291	12	�	�	PROPN
ejpam-2347	291	13	−m+n	−m+n	PROPN
ejpam-2347	291	14	p	p	PROPN
ejpam-2347	291	15	�	�	PROPN
ejpam-2347	291	16	hp(n−m	hp(n−m	NOUN
ejpam-2347	291	17	)	)	PUNCT
ejpam-2347	291	18	hp(n	hp(n	X
ejpam-2347	291	19	)	)	PUNCT
ejpam-2347	291	20	bp(n−m	bp(n−m	PROPN
ejpam-2347	291	21	,	,	PUNCT
ejpam-2347	291	22	m	m	PROPN
ejpam-2347	291	23	)	)	PUNCT
ejpam-2347	291	24	if	if	SCONJ
ejpam-2347	291	25	m	m	VERB
ejpam-2347	291	26	<	<	X
ejpam-2347	291	27	n	n	X
ejpam-2347	291	28	(	(	PUNCT
ejpam-2347	291	29	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	291	30	�	�	PROPN
ejpam-2347	291	31	n	n	CCONJ
ejpam-2347	291	32	p	p	PROPN
ejpam-2347	291	33	�	�	PROPN
ejpam-2347	291	34	1	1	NUM
ejpam-2347	291	35	hp(n	hp(n	NUM
ejpam-2347	291	36	)	)	PUNCT
ejpam-2347	291	37	(	(	PUNCT
ejpam-2347	291	38	bp(m−	bp(m−	PROPN
ejpam-2347	291	39	n	n	CCONJ
ejpam-2347	291	40	,	,	PUNCT
ejpam-2347	291	41	n))−1	n))−1	NOUN
ejpam-2347	291	42	if	if	SCONJ
ejpam-2347	291	43	n≤	n≤	PRON
ejpam-2347	291	44	m	m	PROPN
ejpam-2347	291	45	h.	h.	PROPN
ejpam-2347	291	46	menken	menken	PROPN
ejpam-2347	291	47	,	,	PUNCT
ejpam-2347	291	48	ö.	ö.	VERB
ejpam-2347	291	49	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	291	50	/	/	SYM
ejpam-2347	291	51	eur	eur	PROPN
ejpam-2347	291	52	.	.	PUNCT
ejpam-2347	292	1	j.	j.	PROPN
ejpam-2347	292	2	pure	pure	PROPN
ejpam-2347	292	3	appl	appl	PROPN
ejpam-2347	292	4	.	.	PROPN
ejpam-2347	292	5	math	math	PROPN
ejpam-2347	292	6	,	,	PUNCT
ejpam-2347	292	7	8	8	NUM
ejpam-2347	292	8	(	(	PUNCT
ejpam-2347	292	9	2015	2015	NUM
ejpam-2347	292	10	)	)	PUNCT
ejpam-2347	292	11	,	,	PUNCT
ejpam-2347	292	12	214	214	NUM
ejpam-2347	292	13	-	-	SYM
ejpam-2347	292	14	231	231	NUM
ejpam-2347	292	15	227	227	NUM
ejpam-2347	292	16	proof	proof	NOUN
ejpam-2347	292	17	.	.	PUNCT
ejpam-2347	293	1	we	we	PRON
ejpam-2347	293	2	know	know	VERB
ejpam-2347	293	3	that	that	SCONJ
ejpam-2347	293	4	bp(−n	bp(−n	NOUN
ejpam-2347	293	5	,	,	PUNCT
ejpam-2347	293	6	m	m	NOUN
ejpam-2347	293	7	)	)	PUNCT
ejpam-2347	293	8	=	=	SYM
ejpam-2347	293	9	γp(−n)γp(m	γp(−n)γp(m	PROPN
ejpam-2347	293	10	)	)	PUNCT
ejpam-2347	293	11	γp(−n+m	γp(−n+m	PROPN
ejpam-2347	293	12	)	)	PUNCT
ejpam-2347	293	13	.	.	PUNCT
ejpam-2347	294	1	assume	assume	VERB
ejpam-2347	294	2	that	that	SCONJ
ejpam-2347	294	3	m	m	PUNCT
ejpam-2347	294	4	<	<	X
ejpam-2347	294	5	n.	n.	NOUN
ejpam-2347	294	6	then	then	ADV
ejpam-2347	294	7	,	,	PUNCT
ejpam-2347	294	8	by	by	ADP
ejpam-2347	294	9	proposition	proposition	NOUN
ejpam-2347	294	10	2	2	NUM
ejpam-2347	294	11	we	we	PRON
ejpam-2347	294	12	can	can	AUX
ejpam-2347	294	13	write	write	VERB
ejpam-2347	294	14	bp(−n	bp(−n	NOUN
ejpam-2347	294	15	,	,	PUNCT
ejpam-2347	294	16	m	m	NOUN
ejpam-2347	294	17	)	)	PUNCT
ejpam-2347	295	1	=	=	SYM
ejpam-2347	295	2	(	(	PUNCT
ejpam-2347	295	3	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	295	4	�	�	PROPN
ejpam-2347	295	5	n	n	CCONJ
ejpam-2347	295	6	p	p	PROPN
ejpam-2347	295	7	�	�	PROPN
ejpam-2347	295	8	(	(	PUNCT
ejpam-2347	295	9	γp(n+	γp(n+	ADP
ejpam-2347	295	10	1))−1γp(m	1))−1γp(m	NUM
ejpam-2347	295	11	)	)	PUNCT
ejpam-2347	295	12	(	(	PUNCT
ejpam-2347	295	13	−1)−m+n+1−	−1)−m+n+1−	NOUN
ejpam-2347	295	14	�	�	VERB
ejpam-2347	295	15	−m+n	−m+n	PROPN
ejpam-2347	295	16	p	p	PROPN
ejpam-2347	295	17	�	�	PROPN
ejpam-2347	295	18	(	(	PUNCT
ejpam-2347	295	19	γp(−m+	γp(−m+	PROPN
ejpam-2347	295	20	n+	n+	NUM
ejpam-2347	295	21	1))−1	1))−1	NUM
ejpam-2347	295	22	=(	=(	NOUN
ejpam-2347	295	23	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	295	24	�	�	PROPN
ejpam-2347	295	25	n	n	CCONJ
ejpam-2347	295	26	p	p	PROPN
ejpam-2347	295	27	�	�	PROPN
ejpam-2347	295	28	+	+	PROPN
ejpam-2347	295	29	m−n−1	m−n−1	PROPN
ejpam-2347	295	30	+	+	SYM
ejpam-2347	295	31	�	�	PROPN
ejpam-2347	295	32	−m+n	−m+n	PROPN
ejpam-2347	295	33	p	p	PROPN
ejpam-2347	295	34	�	�	PROPN
ejpam-2347	295	35	γp(n−m+	γp(n−m+	PROPN
ejpam-2347	295	36	1)γp(m	1)γp(m	NUM
ejpam-2347	295	37	)	)	PUNCT
ejpam-2347	295	38	γp(n+	γp(n+	ADP
ejpam-2347	295	39	1	1	NUM
ejpam-2347	295	40	)	)	PUNCT
ejpam-2347	295	41	.	.	PUNCT
ejpam-2347	296	1	using	use	VERB
ejpam-2347	296	2	proposition	proposition	NOUN
ejpam-2347	296	3	1	1	NUM
ejpam-2347	296	4	we	we	PRON
ejpam-2347	296	5	obtain	obtain	VERB
ejpam-2347	296	6	bp(−n	bp(−n	NOUN
ejpam-2347	296	7	,	,	PUNCT
ejpam-2347	296	8	m	m	NOUN
ejpam-2347	296	9	)	)	PUNCT
ejpam-2347	296	10	=(	=(	PROPN
ejpam-2347	296	11	−1)m−	−1)m−	X
ejpam-2347	296	12	�	�	PROPN
ejpam-2347	296	13	n	n	CCONJ
ejpam-2347	296	14	p	p	PROPN
ejpam-2347	296	15	�	�	PROPN
ejpam-2347	296	16	+	+	CCONJ
ejpam-2347	296	17	�	�	PROPN
ejpam-2347	296	18	−m+n	−m+n	PROPN
ejpam-2347	296	19	p	p	PROPN
ejpam-2347	296	20	�	�	PROPN
ejpam-2347	296	21	γp(n−m)hp(n−m)γp(m	γp(n−m)hp(n−m)γp(m	ADJ
ejpam-2347	296	22	)	)	PUNCT
ejpam-2347	296	23	γp(n)hp(n	γp(n)hp(n	PROPN
ejpam-2347	296	24	)	)	PUNCT
ejpam-2347	296	25	=(	=(	PROPN
ejpam-2347	296	26	−1)m−	−1)m−	X
ejpam-2347	296	27	�	�	PROPN
ejpam-2347	296	28	n	n	CCONJ
ejpam-2347	296	29	p	p	PROPN
ejpam-2347	296	30	�	�	PROPN
ejpam-2347	296	31	+	+	CCONJ
ejpam-2347	296	32	�	�	PROPN
ejpam-2347	296	33	−m+n	−m+n	PROPN
ejpam-2347	296	34	p	p	PROPN
ejpam-2347	296	35	�	�	PROPN
ejpam-2347	296	36	hp(n−m	hp(n−m	NOUN
ejpam-2347	296	37	)	)	PUNCT
ejpam-2347	296	38	hp(n	hp(n	NUM
ejpam-2347	296	39	)	)	PUNCT
ejpam-2347	296	40	bp(n−m	bp(n−m	PROPN
ejpam-2347	296	41	,	,	PUNCT
ejpam-2347	296	42	m	m	PROPN
ejpam-2347	296	43	)	)	PUNCT
ejpam-2347	296	44	.	.	PUNCT
ejpam-2347	297	1	assume	assume	VERB
ejpam-2347	297	2	that	that	SCONJ
ejpam-2347	297	3	n≤	n≤	PRON
ejpam-2347	297	4	m.	m.	NOUN
ejpam-2347	297	5	by	by	ADP
ejpam-2347	297	6	proposition	proposition	NOUN
ejpam-2347	297	7	2	2	NUM
ejpam-2347	297	8	we	we	PRON
ejpam-2347	297	9	get	get	VERB
ejpam-2347	297	10	bp(−n	bp(−n	ADJ
ejpam-2347	297	11	,	,	PUNCT
ejpam-2347	297	12	m	m	NOUN
ejpam-2347	297	13	)	)	PUNCT
ejpam-2347	297	14	=	=	SYM
ejpam-2347	297	15	(	(	PUNCT
ejpam-2347	297	16	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	297	17	�	�	PROPN
ejpam-2347	297	18	n	n	CCONJ
ejpam-2347	297	19	p	p	PROPN
ejpam-2347	297	20	�	�	PROPN
ejpam-2347	297	21	(	(	PUNCT
ejpam-2347	297	22	γp(n+	γp(n+	NOUN
ejpam-2347	297	23	1))−1γp(m	1))−1γp(m	NUM
ejpam-2347	297	24	)	)	PUNCT
ejpam-2347	297	25	γp(m−	γp(m−	PROPN
ejpam-2347	297	26	n	n	CCONJ
ejpam-2347	297	27	)	)	PUNCT
ejpam-2347	297	28	=(	=(	NOUN
ejpam-2347	297	29	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	297	30	�	�	PROPN
ejpam-2347	297	31	n	n	CCONJ
ejpam-2347	297	32	p	p	PROPN
ejpam-2347	297	33	�	�	PROPN
ejpam-2347	297	34	γp(m	γp(m	PROPN
ejpam-2347	297	35	)	)	PUNCT
ejpam-2347	297	36	γp(m−	γp(m−	PROPN
ejpam-2347	298	1	n)γp(n+	n)γp(n+	PROPN
ejpam-2347	298	2	1	1	NUM
ejpam-2347	298	3	)	)	PUNCT
ejpam-2347	298	4	,	,	PUNCT
ejpam-2347	298	5	and	and	CCONJ
ejpam-2347	298	6	by	by	ADP
ejpam-2347	298	7	proposition	proposition	NOUN
ejpam-2347	298	8	1	1	NUM
ejpam-2347	298	9	we	we	PRON
ejpam-2347	298	10	have	have	VERB
ejpam-2347	298	11	bp(−n	bp(−n	NOUN
ejpam-2347	298	12	,	,	PUNCT
ejpam-2347	298	13	m	m	NOUN
ejpam-2347	298	14	)	)	PUNCT
ejpam-2347	298	15	=(	=(	NOUN
ejpam-2347	298	16	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	298	17	�	�	PROPN
ejpam-2347	298	18	n	n	CCONJ
ejpam-2347	298	19	p	p	PROPN
ejpam-2347	298	20	�	�	PROPN
ejpam-2347	298	21	γp(m	γp(m	PROPN
ejpam-2347	298	22	)	)	PUNCT
ejpam-2347	298	23	γp(m−	γp(m−	PUNCT
ejpam-2347	299	1	n)γp(n)hp(n	n)γp(n)hp(n	X
ejpam-2347	299	2	)	)	PUNCT
ejpam-2347	299	3	=	=	SYM
ejpam-2347	299	4	(	(	PUNCT
ejpam-2347	299	5	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	299	6	�	�	PROPN
ejpam-2347	299	7	n	n	CCONJ
ejpam-2347	299	8	p	p	PROPN
ejpam-2347	299	9	�	�	PROPN
ejpam-2347	299	10	hp(n	hp(n	NUM
ejpam-2347	299	11	)	)	PUNCT
ejpam-2347	299	12	(	(	PUNCT
ejpam-2347	299	13	bp(m−	bp(m−	PROPN
ejpam-2347	299	14	n	n	CCONJ
ejpam-2347	299	15	,	,	PUNCT
ejpam-2347	299	16	n))−1	n))−1	NOUN
ejpam-2347	299	17	theorem	theorem	NOUN
ejpam-2347	299	18	13	13	NUM
ejpam-2347	299	19	.	.	PUNCT
ejpam-2347	300	1	if	if	SCONJ
ejpam-2347	300	2	n	n	CCONJ
ejpam-2347	300	3	,	,	PUNCT
ejpam-2347	300	4	m	m	VERB
ejpam-2347	300	5	∈	∈	PROPN
ejpam-2347	300	6	n	n	NOUN
ejpam-2347	300	7	then	then	ADV
ejpam-2347	300	8	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	300	9	)	)	PUNCT
ejpam-2347	300	10	=	=	PUNCT
ejpam-2347	300	11			PROPN
ejpam-2347	300	12			VERB
ejpam-2347	300	13			PRON
ejpam-2347	300	14			ADJ
ejpam-2347	300	15			PROPN
ejpam-2347	300	16	(	(	PUNCT
ejpam-2347	300	17	−1)m+1−[m	−1)m+1−[m	X
ejpam-2347	300	18	p	p	X
ejpam-2347	300	19	]	]	X
ejpam-2347	300	20	hp(m	hp(m	X
ejpam-2347	300	21	)	)	PUNCT
ejpam-2347	300	22	bp(n−m	bp(n−m	PROPN
ejpam-2347	300	23	,	,	PUNCT
ejpam-2347	300	24	m)−1	m)−1	NOUN
ejpam-2347	300	25	if	if	SCONJ
ejpam-2347	300	26	m≤	m≤	PROPN
ejpam-2347	300	27	n	n	INTJ
ejpam-2347	300	28	(	(	PUNCT
ejpam-2347	300	29	−1)n−	−1)n−	X
ejpam-2347	300	30	[	[	PUNCT
ejpam-2347	300	31	m	m	NOUN
ejpam-2347	300	32	p	p	X
ejpam-2347	300	33	]	]	X
ejpam-2347	301	1	+	+	PROPN
ejpam-2347	301	2	[	[	X
ejpam-2347	301	3	m−n	m−n	NOUN
ejpam-2347	301	4	p	p	X
ejpam-2347	301	5	]	]	X
ejpam-2347	301	6	hp(m−n	hp(m−n	PROPN
ejpam-2347	301	7	)	)	PUNCT
ejpam-2347	301	8	hp(m	hp(m	X
ejpam-2347	301	9	)	)	PUNCT
ejpam-2347	301	10	bp(m−	bp(m−	PROPN
ejpam-2347	301	11	n	n	CCONJ
ejpam-2347	301	12	,	,	PUNCT
ejpam-2347	301	13	n	n	CCONJ
ejpam-2347	301	14	)	)	PUNCT
ejpam-2347	301	15	if	if	SCONJ
ejpam-2347	301	16	n	n	CCONJ
ejpam-2347	301	17	<	<	X
ejpam-2347	301	18	m	m	PROPN
ejpam-2347	301	19	h.	h.	PROPN
ejpam-2347	301	20	menken	menken	PROPN
ejpam-2347	301	21	,	,	PUNCT
ejpam-2347	301	22	ö.	ö.	VERB
ejpam-2347	301	23	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	301	24	/	/	SYM
ejpam-2347	301	25	eur	eur	PROPN
ejpam-2347	301	26	.	.	PUNCT
ejpam-2347	302	1	j.	j.	PROPN
ejpam-2347	302	2	pure	pure	PROPN
ejpam-2347	302	3	appl	appl	PROPN
ejpam-2347	302	4	.	.	PROPN
ejpam-2347	302	5	math	math	PROPN
ejpam-2347	302	6	,	,	PUNCT
ejpam-2347	302	7	8	8	NUM
ejpam-2347	302	8	(	(	PUNCT
ejpam-2347	302	9	2015	2015	NUM
ejpam-2347	302	10	)	)	PUNCT
ejpam-2347	302	11	,	,	PUNCT
ejpam-2347	302	12	214	214	NUM
ejpam-2347	302	13	-	-	SYM
ejpam-2347	302	14	231	231	NUM
ejpam-2347	302	15	228	228	NUM
ejpam-2347	302	16	proof	proof	NOUN
ejpam-2347	302	17	.	.	PUNCT
ejpam-2347	303	1	from	from	ADP
ejpam-2347	303	2	definition	definition	NOUN
ejpam-2347	303	3	2	2	NUM
ejpam-2347	303	4	we	we	PRON
ejpam-2347	303	5	write	write	VERB
ejpam-2347	303	6	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	303	7	)	)	PUNCT
ejpam-2347	303	8	=	=	SYM
ejpam-2347	303	9	γp(n)γp(−m	γp(n)γp(−m	NOUN
ejpam-2347	303	10	)	)	PUNCT
ejpam-2347	303	11	γp(n−m	γp(n−m	NUM
ejpam-2347	303	12	)	)	PUNCT
ejpam-2347	303	13	.	.	PUNCT
ejpam-2347	304	1	if	if	SCONJ
ejpam-2347	304	2	m≤	m≤	PROPN
ejpam-2347	304	3	n	n	CCONJ
ejpam-2347	304	4	,	,	PUNCT
ejpam-2347	304	5	using	use	VERB
ejpam-2347	304	6	proposition	proposition	NOUN
ejpam-2347	304	7	2	2	NUM
ejpam-2347	304	8	we	we	PRON
ejpam-2347	304	9	get	get	VERB
ejpam-2347	304	10	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	304	11	)	)	PUNCT
ejpam-2347	304	12	=	=	SYM
ejpam-2347	305	1	γp(n)(−1)m+1−	γp(n)(−1)m+1−	PROPN
ejpam-2347	305	2	�	�	PROPN
ejpam-2347	305	3	m	m	PROPN
ejpam-2347	305	4	p	p	NOUN
ejpam-2347	305	5	�	�	PROPN
ejpam-2347	305	6	γp(m+	γp(m+	PROPN
ejpam-2347	305	7	1)−1	1)−1	NUM
ejpam-2347	305	8	γp(n−m	γp(n−m	NUM
ejpam-2347	305	9	)	)	PUNCT
ejpam-2347	305	10	=(	=(	NOUN
ejpam-2347	305	11	−1)m+1−	−1)m+1−	X
ejpam-2347	305	12	�	�	PROPN
ejpam-2347	305	13	m	m	PROPN
ejpam-2347	305	14	p	p	PROPN
ejpam-2347	305	15	�	�	PROPN
ejpam-2347	305	16	γp(n	γp(n	NOUN
ejpam-2347	305	17	)	)	PUNCT
ejpam-2347	305	18	γp(m+	γp(m+	NOUN
ejpam-2347	305	19	1)γp(n−m	1)γp(n−m	NUM
ejpam-2347	305	20	)	)	PUNCT
ejpam-2347	305	21	.	.	PUNCT
ejpam-2347	306	1	according	accord	VERB
ejpam-2347	306	2	to	to	ADP
ejpam-2347	306	3	proposition	proposition	NOUN
ejpam-2347	306	4	1	1	NUM
ejpam-2347	306	5	and	and	CCONJ
ejpam-2347	306	6	definition	definition	NOUN
ejpam-2347	306	7	2	2	NUM
ejpam-2347	306	8	we	we	PRON
ejpam-2347	306	9	have	have	VERB
ejpam-2347	306	10	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	306	11	)	)	PUNCT
ejpam-2347	306	12	=(	=(	NOUN
ejpam-2347	306	13	−1)m+1−	−1)m+1−	PROPN
ejpam-2347	306	14	�	�	PROPN
ejpam-2347	306	15	m	m	PROPN
ejpam-2347	306	16	p	p	PROPN
ejpam-2347	306	17	�	�	PROPN
ejpam-2347	306	18	γp(n	γp(n	NOUN
ejpam-2347	306	19	)	)	PUNCT
ejpam-2347	306	20	γp(m)hp(m)γp(n−m	γp(m)hp(m)γp(n−m	PROPN
ejpam-2347	306	21	)	)	PUNCT
ejpam-2347	306	22	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	306	23	)	)	PUNCT
ejpam-2347	306	24	=	=	PUNCT
ejpam-2347	306	25	(	(	PUNCT
ejpam-2347	306	26	−1)m+1−	−1)m+1−	PROPN
ejpam-2347	306	27	�	�	PROPN
ejpam-2347	306	28	m	m	PROPN
ejpam-2347	306	29	p	p	PROPN
ejpam-2347	306	30	�	�	PROPN
ejpam-2347	306	31	hp(m	hp(m	PART
ejpam-2347	306	32	)	)	PUNCT
ejpam-2347	307	1	bp(n−m	bp(n−m	PROPN
ejpam-2347	307	2	,	,	PUNCT
ejpam-2347	307	3	m)−1	m)−1	NOUN
ejpam-2347	307	4	.	.	PUNCT
ejpam-2347	308	1	if	if	SCONJ
ejpam-2347	308	2	n	n	CCONJ
ejpam-2347	308	3	<	<	X
ejpam-2347	308	4	m	m	PROPN
ejpam-2347	308	5	,	,	PUNCT
ejpam-2347	308	6	then	then	ADV
ejpam-2347	308	7	by	by	ADP
ejpam-2347	308	8	proposition	proposition	NOUN
ejpam-2347	308	9	2	2	NUM
ejpam-2347	308	10	we	we	PRON
ejpam-2347	308	11	have	have	VERB
ejpam-2347	308	12	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	308	13	)	)	PUNCT
ejpam-2347	309	1	=	=	SYM
ejpam-2347	309	2	γp(n)(−1)m+1−	γp(n)(−1)m+1−	PROPN
ejpam-2347	309	3	�	�	PROPN
ejpam-2347	309	4	m	m	PROPN
ejpam-2347	309	5	p	p	PROPN
ejpam-2347	309	6	�	�	PROPN
ejpam-2347	309	7	γp(m+	γp(m+	NOUN
ejpam-2347	309	8	1)−1	1)−1	NUM
ejpam-2347	309	9	(	(	PUNCT
ejpam-2347	309	10	−1)(m−n)+1−	−1)(m−n)+1−	PROPN
ejpam-2347	309	11	�	�	PROPN
ejpam-2347	309	12	m−n	m−n	PROPN
ejpam-2347	309	13	p	p	PROPN
ejpam-2347	309	14	�	�	PROPN
ejpam-2347	309	15	γp(m−	γp(m−	PUNCT
ejpam-2347	309	16	n+	n+	PUNCT
ejpam-2347	310	1	1)−1	1)−1	NUM
ejpam-2347	310	2	=(	=(	NOUN
ejpam-2347	310	3	−1)m+1−	−1)m+1−	X
ejpam-2347	310	4	�	�	PROPN
ejpam-2347	310	5	m	m	PROPN
ejpam-2347	310	6	p	p	PROPN
ejpam-2347	310	7	�	�	PROPN
ejpam-2347	310	8	−(m−n)−1	−(m−n)−1	PROPN
ejpam-2347	310	9	+	+	PROPN
ejpam-2347	310	10	�	�	PROPN
ejpam-2347	310	11	m−n	m−n	PROPN
ejpam-2347	310	12	p	p	PROPN
ejpam-2347	310	13	�	�	PROPN
ejpam-2347	310	14	γp(n)γp(m−	γp(n)γp(m−	PROPN
ejpam-2347	310	15	n+	n+	PUNCT
ejpam-2347	310	16	1	1	NUM
ejpam-2347	310	17	)	)	PUNCT
ejpam-2347	310	18	γp(m+	γp(m+	NOUN
ejpam-2347	310	19	1	1	NUM
ejpam-2347	310	20	)	)	PUNCT
ejpam-2347	310	21	.	.	PUNCT
ejpam-2347	311	1	using	use	VERB
ejpam-2347	311	2	proposition	proposition	NOUN
ejpam-2347	311	3	1	1	NUM
ejpam-2347	311	4	and	and	CCONJ
ejpam-2347	311	5	definition	definition	NOUN
ejpam-2347	311	6	2	2	NUM
ejpam-2347	311	7	we	we	PRON
ejpam-2347	311	8	obtain	obtain	VERB
ejpam-2347	311	9	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	311	10	)	)	PUNCT
ejpam-2347	311	11	=(	=(	NOUN
ejpam-2347	311	12	−1)n−	−1)n−	X
ejpam-2347	311	13	�	�	PROPN
ejpam-2347	311	14	m	m	PROPN
ejpam-2347	311	15	p	p	PROPN
ejpam-2347	311	16	�	�	PROPN
ejpam-2347	311	17	+	+	CCONJ
ejpam-2347	311	18	�	�	PROPN
ejpam-2347	311	19	m−n	m−n	PROPN
ejpam-2347	311	20	p	p	PROPN
ejpam-2347	311	21	�	�	PROPN
ejpam-2347	311	22	γp(n)γp(m−	γp(n)γp(m−	PROPN
ejpam-2347	311	23	n)hp(m−	n)hp(m−	PRON
ejpam-2347	311	24	n	n	CCONJ
ejpam-2347	311	25	)	)	PUNCT
ejpam-2347	311	26	γp(m)hp(m	γp(m)hp(m	NOUN
ejpam-2347	311	27	)	)	PUNCT
ejpam-2347	311	28	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	311	29	)	)	PUNCT
ejpam-2347	311	30	=	=	SYM
ejpam-2347	311	31	(	(	PUNCT
ejpam-2347	311	32	−1)n−	−1)n−	X
ejpam-2347	311	33	�	�	PROPN
ejpam-2347	311	34	m	m	PROPN
ejpam-2347	311	35	p	p	PROPN
ejpam-2347	311	36	�	�	PROPN
ejpam-2347	311	37	+	+	CCONJ
ejpam-2347	311	38	�	�	PROPN
ejpam-2347	311	39	m−n	m−n	PROPN
ejpam-2347	311	40	p	p	PROPN
ejpam-2347	311	41	�	�	PROPN
ejpam-2347	311	42	hp(m−	hp(m−	PROPN
ejpam-2347	311	43	n	n	CCONJ
ejpam-2347	311	44	)	)	PUNCT
ejpam-2347	311	45	hp(m	hp(m	PROPN
ejpam-2347	311	46	)	)	PUNCT
ejpam-2347	311	47	bp(m−	bp(m−	PROPN
ejpam-2347	311	48	n	n	CCONJ
ejpam-2347	311	49	,	,	PUNCT
ejpam-2347	311	50	n	n	CCONJ
ejpam-2347	311	51	)	)	PUNCT
ejpam-2347	311	52	.	.	PUNCT
ejpam-2347	312	1	3	3	X
ejpam-2347	312	2	.	.	X
ejpam-2347	312	3	conclusions	conclusion	NOUN
ejpam-2347	312	4	in	in	ADP
ejpam-2347	312	5	the	the	DET
ejpam-2347	312	6	present	present	ADJ
ejpam-2347	312	7	work	work	NOUN
ejpam-2347	312	8	we	we	PRON
ejpam-2347	312	9	prove	prove	VERB
ejpam-2347	312	10	that	that	SCONJ
ejpam-2347	312	11	the	the	DET
ejpam-2347	312	12	p	p	NOUN
ejpam-2347	312	13	-	-	PUNCT
ejpam-2347	312	14	adic	adic	ADJ
ejpam-2347	312	15	beta	beta	NOUN
ejpam-2347	312	16	function	function	NOUN
ejpam-2347	312	17	bp	bp	PROPN
ejpam-2347	312	18	:	:	PUNCT
ejpam-2347	312	19	zp	zp	PROPN
ejpam-2347	312	20	×	×	PROPN
ejpam-2347	312	21	zp	zp	PROPN
ejpam-2347	312	22	→	→	PUNCT
ejpam-2347	312	23	qp	qp	PROPN
ejpam-2347	312	24	has	have	VERB
ejpam-2347	312	25	the	the	DET
ejpam-2347	312	26	following	follow	VERB
ejpam-2347	312	27	properties	property	NOUN
ejpam-2347	312	28	:	:	PUNCT
ejpam-2347	312	29	•	•	ADP
ejpam-2347	312	30	if	if	SCONJ
ejpam-2347	312	31	x	x	X
ejpam-2347	312	32	,	,	PUNCT
ejpam-2347	312	33	y	y	PROPN
ejpam-2347	312	34	∈	∈	PROPN
ejpam-2347	312	35	zp	zp	PROPN
ejpam-2347	312	36	,	,	PUNCT
ejpam-2347	312	37	then	then	ADV
ejpam-2347	312	38	bp(x	bp(x	NOUN
ejpam-2347	312	39	,	,	PUNCT
ejpam-2347	312	40	y	y	PROPN
ejpam-2347	312	41	)	)	PUNCT
ejpam-2347	312	42	=	=	PUNCT
ejpam-2347	312	43	bp(y	bp(y	X
ejpam-2347	312	44	,	,	PUNCT
ejpam-2347	312	45	x	x	X
ejpam-2347	312	46	)	)	PUNCT
ejpam-2347	312	47	h.	h.	PROPN
ejpam-2347	312	48	menken	menken	PROPN
ejpam-2347	312	49	,	,	PUNCT
ejpam-2347	312	50	ö.	ö.	VERB
ejpam-2347	312	51	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	312	52	/	/	SYM
ejpam-2347	312	53	eur	eur	PROPN
ejpam-2347	312	54	.	.	PUNCT
ejpam-2347	313	1	j.	j.	PROPN
ejpam-2347	313	2	pure	pure	PROPN
ejpam-2347	313	3	appl	appl	PROPN
ejpam-2347	313	4	.	.	PROPN
ejpam-2347	313	5	math	math	PROPN
ejpam-2347	313	6	,	,	PUNCT
ejpam-2347	313	7	8	8	NUM
ejpam-2347	313	8	(	(	PUNCT
ejpam-2347	313	9	2015	2015	NUM
ejpam-2347	313	10	)	)	PUNCT
ejpam-2347	313	11	,	,	PUNCT
ejpam-2347	313	12	214	214	NUM
ejpam-2347	313	13	-	-	SYM
ejpam-2347	313	14	231	231	NUM
ejpam-2347	313	15	229	229	NUM
ejpam-2347	313	16	•	•	NOUN
ejpam-2347	313	17	if	if	SCONJ
ejpam-2347	313	18	x	x	PRON
ejpam-2347	313	19	,	,	PUNCT
ejpam-2347	313	20	y	y	PROPN
ejpam-2347	313	21	∈	∈	PROPN
ejpam-2347	313	22	zp	zp	PROPN
ejpam-2347	313	23	,	,	PUNCT
ejpam-2347	313	24	then	then	ADV
ejpam-2347	313	25	bp(x	bp(x	NOUN
ejpam-2347	313	26	,	,	PUNCT
ejpam-2347	313	27	y)bp(x	y)bp(x	ADJ
ejpam-2347	313	28	+	+	NOUN
ejpam-2347	313	29	y	y	NOUN
ejpam-2347	313	30	,	,	PUNCT
ejpam-2347	313	31	1−	1−	NUM
ejpam-2347	313	32	y	y	NOUN
ejpam-2347	313	33	)	)	PUNCT
ejpam-2347	313	34	=	=	PUNCT
ejpam-2347	314	1			PROPN
ejpam-2347	314	2			PROPN
ejpam-2347	314	3			PROPN
ejpam-2347	314	4	(	(	PUNCT
ejpam-2347	314	5	−1)ℓ(y	−1)ℓ(y	PROPN
ejpam-2347	314	6	)	)	PUNCT
ejpam-2347	314	7	hp(x	hp(x	PROPN
ejpam-2347	314	8	)	)	PUNCT
ejpam-2347	314	9	,	,	PUNCT
ejpam-2347	314	10	p	p	X
ejpam-2347	314	11	6=	6=	ADP
ejpam-2347	314	12	2	2	NUM
ejpam-2347	314	13	(	(	PUNCT
ejpam-2347	314	14	−1)σ(y)+1	−1)σ(y)+1	NOUN
ejpam-2347	314	15	hp(x	hp(x	NOUN
ejpam-2347	314	16	)	)	PUNCT
ejpam-2347	314	17	p	p	X
ejpam-2347	315	1	=	=	SYM
ejpam-2347	315	2	2	2	NUM
ejpam-2347	315	3	•	•	NOUN
ejpam-2347	315	4	if	if	SCONJ
ejpam-2347	315	5	x	x	X
ejpam-2347	315	6	,	,	PUNCT
ejpam-2347	315	7	y	y	PROPN
ejpam-2347	315	8	∈	∈	PROPN
ejpam-2347	315	9	zp	zp	PROPN
ejpam-2347	315	10	,	,	PUNCT
ejpam-2347	315	11	then	then	ADV
ejpam-2347	315	12	bp(x	bp(x	PUNCT
ejpam-2347	315	13	+	+	PROPN
ejpam-2347	315	14	1	1	NUM
ejpam-2347	315	15	,	,	PUNCT
ejpam-2347	315	16	y	y	NOUN
ejpam-2347	315	17	)	)	PUNCT
ejpam-2347	315	18	=	=	SYM
ejpam-2347	315	19	hp(x	hp(x	PROPN
ejpam-2347	315	20	)	)	PUNCT
ejpam-2347	315	21	hp(x	hp(x	PROPN
ejpam-2347	315	22	+	+	PROPN
ejpam-2347	315	23	y	y	NOUN
ejpam-2347	315	24	)	)	PUNCT
ejpam-2347	315	25	bp(x	bp(x	NOUN
ejpam-2347	315	26	,	,	PUNCT
ejpam-2347	315	27	y	y	PROPN
ejpam-2347	315	28	)	)	PUNCT
ejpam-2347	315	29	•	•	NOUN
ejpam-2347	315	30	if	if	SCONJ
ejpam-2347	315	31	x	x	PRON
ejpam-2347	315	32	,	,	PUNCT
ejpam-2347	315	33	y	y	PROPN
ejpam-2347	315	34	∈	∈	PROPN
ejpam-2347	315	35	zp	zp	PROPN
ejpam-2347	315	36	,	,	PUNCT
ejpam-2347	315	37	then	then	ADV
ejpam-2347	315	38	bp(x	bp(x	PUNCT
ejpam-2347	315	39	,	,	PUNCT
ejpam-2347	315	40	y	y	PROPN
ejpam-2347	315	41	+	+	NOUN
ejpam-2347	315	42	1	1	X
ejpam-2347	315	43	)	)	PUNCT
ejpam-2347	315	44	=	=	NOUN
ejpam-2347	315	45	hp(y	hp(y	X
ejpam-2347	315	46	)	)	PUNCT
ejpam-2347	315	47	hp(x	hp(x	PROPN
ejpam-2347	315	48	+	+	PROPN
ejpam-2347	315	49	y	y	NOUN
ejpam-2347	315	50	)	)	PUNCT
ejpam-2347	315	51	bp(x	bp(x	NOUN
ejpam-2347	315	52	,	,	PUNCT
ejpam-2347	315	53	y	y	PROPN
ejpam-2347	315	54	)	)	PUNCT
ejpam-2347	315	55	•	•	NOUN
ejpam-2347	316	1	if	if	SCONJ
ejpam-2347	316	2	x	x	PRON
ejpam-2347	316	3	,	,	PUNCT
ejpam-2347	316	4	y	y	PROPN
ejpam-2347	316	5	∈	∈	PROPN
ejpam-2347	316	6	zp	zp	PROPN
ejpam-2347	316	7	,	,	PUNCT
ejpam-2347	316	8	then	then	ADV
ejpam-2347	316	9	bp(x	bp(x	PUNCT
ejpam-2347	316	10	+	+	PROPN
ejpam-2347	316	11	1	1	NUM
ejpam-2347	316	12	,	,	PUNCT
ejpam-2347	316	13	y	y	PROPN
ejpam-2347	316	14	)	)	PUNCT
ejpam-2347	316	15	+	+	CCONJ
ejpam-2347	316	16	bp(x	bp(x	X
ejpam-2347	316	17	,	,	PUNCT
ejpam-2347	316	18	y	y	PROPN
ejpam-2347	316	19	+	+	NOUN
ejpam-2347	316	20	1	1	X
ejpam-2347	316	21	)	)	PUNCT
ejpam-2347	316	22	=	=	SYM
ejpam-2347	316	23	hp(x	hp(x	PROPN
ejpam-2347	316	24	)	)	PUNCT
ejpam-2347	316	25	+	+	NUM
ejpam-2347	316	26	hp(y	hp(y	NOUN
ejpam-2347	316	27	)	)	PUNCT
ejpam-2347	316	28	hp(x	hp(x	PROPN
ejpam-2347	316	29	+	+	PROPN
ejpam-2347	316	30	y	y	NOUN
ejpam-2347	316	31	)	)	PUNCT
ejpam-2347	316	32	bp(x	bp(x	NOUN
ejpam-2347	316	33	,	,	PUNCT
ejpam-2347	316	34	y	y	PROPN
ejpam-2347	316	35	)	)	PUNCT
ejpam-2347	316	36	•	•	NOUN
ejpam-2347	317	1	if	if	SCONJ
ejpam-2347	317	2	x	x	PRON
ejpam-2347	317	3	,	,	PUNCT
ejpam-2347	317	4	y	y	PROPN
ejpam-2347	317	5	∈	∈	PROPN
ejpam-2347	317	6	zp	zp	PROPN
ejpam-2347	317	7	,	,	PUNCT
ejpam-2347	317	8	then	then	ADV
ejpam-2347	317	9	bp(x	bp(x	PUNCT
ejpam-2347	317	10	,	,	PUNCT
ejpam-2347	317	11	y	y	PROPN
ejpam-2347	317	12	+	+	NOUN
ejpam-2347	317	13	1	1	X
ejpam-2347	317	14	)	)	PUNCT
ejpam-2347	317	15	=	=	NOUN
ejpam-2347	317	16	hp(y	hp(y	X
ejpam-2347	317	17	)	)	PUNCT
ejpam-2347	317	18	hp(x	hp(x	NOUN
ejpam-2347	317	19	)	)	PUNCT
ejpam-2347	317	20	bp(x	bp(x	NOUN
ejpam-2347	317	21	+	+	NOUN
ejpam-2347	317	22	1	1	NUM
ejpam-2347	317	23	,	,	PUNCT
ejpam-2347	317	24	y	y	NOUN
ejpam-2347	317	25	)	)	PUNCT
ejpam-2347	317	26	•	•	NOUN
ejpam-2347	317	27	if	if	SCONJ
ejpam-2347	317	28	x	x	PRON
ejpam-2347	317	29	,	,	PUNCT
ejpam-2347	317	30	y	y	PROPN
ejpam-2347	317	31	∈	∈	PROPN
ejpam-2347	317	32	zp	zp	PROPN
ejpam-2347	317	33	,	,	PUNCT
ejpam-2347	317	34	then	then	ADV
ejpam-2347	317	35	bp(x	bp(x	PUNCT
ejpam-2347	317	36	+	+	PROPN
ejpam-2347	317	37	1	1	X
ejpam-2347	317	38	,	,	PUNCT
ejpam-2347	317	39	y	y	PROPN
ejpam-2347	317	40	+	+	NOUN
ejpam-2347	317	41	1	1	X
ejpam-2347	317	42	)	)	PUNCT
ejpam-2347	317	43	=	=	SYM
ejpam-2347	317	44	hp(x)hp(y	hp(x)hp(y	X
ejpam-2347	317	45	)	)	PUNCT
ejpam-2347	317	46	hp(x	hp(x	PROPN
ejpam-2347	318	1	+	+	NOUN
ejpam-2347	318	2	y	y	PROPN
ejpam-2347	318	3	+	+	CCONJ
ejpam-2347	318	4	1)hp(x	1)hp(x	NUM
ejpam-2347	319	1	+	+	CCONJ
ejpam-2347	319	2	y	y	NOUN
ejpam-2347	319	3	)	)	PUNCT
ejpam-2347	319	4	bp(x	bp(x	NOUN
ejpam-2347	319	5	,	,	PUNCT
ejpam-2347	319	6	y	y	PROPN
ejpam-2347	319	7	)	)	PUNCT
ejpam-2347	319	8	•	•	NOUN
ejpam-2347	319	9	if	if	SCONJ
ejpam-2347	319	10	x	x	X
ejpam-2347	319	11	,	,	PUNCT
ejpam-2347	319	12	y	y	PROPN
ejpam-2347	319	13	,	,	PUNCT
ejpam-2347	319	14	z	z	PROPN
ejpam-2347	319	15	,	,	PUNCT
ejpam-2347	319	16	w	w	PROPN
ejpam-2347	319	17	∈	∈	PROPN
ejpam-2347	319	18	zp	zp	NOUN
ejpam-2347	319	19	,	,	PUNCT
ejpam-2347	319	20	then	then	ADV
ejpam-2347	319	21	bp(x	bp(x	NOUN
ejpam-2347	319	22	,	,	PUNCT
ejpam-2347	319	23	y)bp(x	y)bp(x	ADJ
ejpam-2347	319	24	+	+	NOUN
ejpam-2347	319	25	y	y	NOUN
ejpam-2347	319	26	,	,	PUNCT
ejpam-2347	319	27	z)bp(x	z)bp(x	X
ejpam-2347	319	28	+	+	NOUN
ejpam-2347	319	29	y	y	PROPN
ejpam-2347	320	1	+	+	PROPN
ejpam-2347	320	2	z	z	PROPN
ejpam-2347	320	3	,	,	PUNCT
ejpam-2347	320	4	w	w	NOUN
ejpam-2347	320	5	)	)	PUNCT
ejpam-2347	320	6	=	=	SYM
ejpam-2347	320	7	γp	γp	PROPN
ejpam-2347	320	8	(	(	PUNCT
ejpam-2347	320	9	x)γp	x)γp	PROPN
ejpam-2347	320	10	�	�	PROPN
ejpam-2347	320	11	y	y	PROPN
ejpam-2347	320	12	�	�	PROPN
ejpam-2347	320	13	γp	γp	PROPN
ejpam-2347	320	14	(	(	PUNCT
ejpam-2347	320	15	z)γp	z)γp	PROPN
ejpam-2347	320	16	(	(	PUNCT
ejpam-2347	320	17	w	w	NOUN
ejpam-2347	320	18	)	)	PUNCT
ejpam-2347	320	19	γp	γp	PROPN
ejpam-2347	320	20	�	�	PROPN
ejpam-2347	320	21	x	x	PUNCT
ejpam-2347	321	1	+	+	PUNCT
ejpam-2347	321	2	y	y	PROPN
ejpam-2347	322	1	+	+	NOUN
ejpam-2347	322	2	z	z	PROPN
ejpam-2347	323	1	+	+	PROPN
ejpam-2347	323	2	w	w	PROPN
ejpam-2347	323	3	�	�	PROPN
ejpam-2347	323	4	•	•	NOUN
ejpam-2347	323	5	if	if	SCONJ
ejpam-2347	323	6	x	x	PROPN
ejpam-2347	323	7	∈	∈	PROPN
ejpam-2347	323	8	zp	zp	NOUN
ejpam-2347	323	9	,	,	PUNCT
ejpam-2347	323	10	then	then	ADV
ejpam-2347	323	11	bp(x	bp(x	NOUN
ejpam-2347	323	12	,	,	PUNCT
ejpam-2347	323	13	1−	1−	NUM
ejpam-2347	323	14	x	x	X
ejpam-2347	323	15	)	)	PUNCT
ejpam-2347	324	1	=	=	SYM
ejpam-2347	324	2	¨	¨	NOUN
ejpam-2347	324	3	(	(	PUNCT
ejpam-2347	324	4	−1)ℓ(x)+1	−1)ℓ(x)+1	NOUN
ejpam-2347	324	5	if	if	SCONJ
ejpam-2347	324	6	p	p	PROPN
ejpam-2347	324	7	6=	6=	NUM
ejpam-2347	324	8	2	2	NUM
ejpam-2347	324	9	(	(	PUNCT
ejpam-2347	324	10	−1)σ1(y)+2	−1)σ1(y)+2	PROPN
ejpam-2347	324	11	if	if	SCONJ
ejpam-2347	324	12	p	p	NOUN
ejpam-2347	324	13	=	=	NOUN
ejpam-2347	324	14	2	2	NUM
ejpam-2347	324	15	•	•	NOUN
ejpam-2347	324	16	if	if	SCONJ
ejpam-2347	324	17	n	n	CCONJ
ejpam-2347	324	18	,	,	PUNCT
ejpam-2347	324	19	k	k	PROPN
ejpam-2347	324	20	∈	∈	PROPN
ejpam-2347	324	21	n	n	CCONJ
ejpam-2347	324	22	,	,	PUNCT
ejpam-2347	324	23	k	k	PROPN
ejpam-2347	324	24	≤	≤	PROPN
ejpam-2347	324	25	n	n	CCONJ
ejpam-2347	324	26	,	,	PUNCT
ejpam-2347	324	27	then	then	ADV
ejpam-2347	324	28	�	�	PROPN
ejpam-2347	324	29	n	n	CCONJ
ejpam-2347	324	30	k	k	PROPN
ejpam-2347	324	31	�	�	PROPN
ejpam-2347	324	32	p	p	PROPN
ejpam-2347	324	33	bp(n−	bp(n−	PROPN
ejpam-2347	324	34	k+	k+	NOUN
ejpam-2347	324	35	1	1	NUM
ejpam-2347	324	36	,	,	PUNCT
ejpam-2347	324	37	k+	k+	NOUN
ejpam-2347	324	38	1	1	NUM
ejpam-2347	324	39	)	)	PUNCT
ejpam-2347	324	40	=	=	VERB
ejpam-2347	324	41	−1	−1	NOUN
ejpam-2347	324	42	hp(n+	hp(n+	NUM
ejpam-2347	324	43	1	1	NUM
ejpam-2347	324	44	)	)	PUNCT
ejpam-2347	324	45	h.	h.	PROPN
ejpam-2347	324	46	menken	menken	PROPN
ejpam-2347	324	47	,	,	PUNCT
ejpam-2347	324	48	ö.	ö.	VERB
ejpam-2347	324	49	çolakoğlu	çolakoğlu	PROPN
ejpam-2347	324	50	/	/	SYM
ejpam-2347	324	51	eur	eur	PROPN
ejpam-2347	324	52	.	.	PUNCT
ejpam-2347	325	1	j.	j.	PROPN
ejpam-2347	325	2	pure	pure	PROPN
ejpam-2347	325	3	appl	appl	PROPN
ejpam-2347	325	4	.	.	PROPN
ejpam-2347	325	5	math	math	PROPN
ejpam-2347	325	6	,	,	PUNCT
ejpam-2347	325	7	8	8	NUM
ejpam-2347	325	8	(	(	PUNCT
ejpam-2347	325	9	2015	2015	NUM
ejpam-2347	325	10	)	)	PUNCT
ejpam-2347	325	11	,	,	PUNCT
ejpam-2347	325	12	214	214	NUM
ejpam-2347	325	13	-	-	SYM
ejpam-2347	325	14	231	231	NUM
ejpam-2347	325	15	230	230	NUM
ejpam-2347	325	16	•	•	NOUN
ejpam-2347	325	17	if	if	SCONJ
ejpam-2347	325	18	m	m	PROPN
ejpam-2347	325	19	,	,	PUNCT
ejpam-2347	325	20	n	n	PROPN
ejpam-2347	325	21	∈	∈	PROPN
ejpam-2347	325	22	n	n	CCONJ
ejpam-2347	325	23	,	,	PUNCT
ejpam-2347	325	24	then	then	ADV
ejpam-2347	325	25	b(n+	b(n+	X
ejpam-2347	325	26	1	1	NUM
ejpam-2347	325	27	,	,	PUNCT
ejpam-2347	325	28	m+	m+	NOUN
ejpam-2347	325	29	1	1	NUM
ejpam-2347	325	30	)	)	PUNCT
ejpam-2347	325	31	=	=	SYM
ejpam-2347	325	32	−bp(n	−bp(n	PROPN
ejpam-2347	325	33	,	,	PUNCT
ejpam-2347	325	34	m	m	NOUN
ejpam-2347	325	35	)	)	PUNCT
ejpam-2347	325	36	hp(n)hp(m	hp(n)hp(m	ADV
ejpam-2347	325	37	)	)	PUNCT
ejpam-2347	325	38	hp(m+	hp(m+	NOUN
ejpam-2347	325	39	n)(m+	n)(m+	NUM
ejpam-2347	325	40	n+	n+	NUM
ejpam-2347	325	41	1	1	NUM
ejpam-2347	325	42	)	)	PUNCT
ejpam-2347	325	43	�	�	PROPN
ejpam-2347	325	44	n	n	CCONJ
ejpam-2347	325	45	p	p	PROPN
ejpam-2347	325	46	�	�	PROPN
ejpam-2347	325	47	!	!	PUNCT
ejpam-2347	326	1	�	�	PROPN
ejpam-2347	326	2	m	m	PROPN
ejpam-2347	326	3	p	p	PROPN
ejpam-2347	326	4	�	�	PROPN
ejpam-2347	326	5	!	!	PUNCT
ejpam-2347	327	1	�	�	PROPN
ejpam-2347	327	2	m+n	m+n	PROPN
ejpam-2347	327	3	p	p	PROPN
ejpam-2347	327	4	�	�	PROPN
ejpam-2347	327	5	!	!	PUNCT
ejpam-2347	328	1	p	p	PRON
ejpam-2347	328	2	�	�	PROPN
ejpam-2347	328	3	n	n	CCONJ
ejpam-2347	328	4	p	p	PROPN
ejpam-2347	328	5	�	�	PROPN
ejpam-2347	328	6	+	+	CCONJ
ejpam-2347	328	7	�	�	PROPN
ejpam-2347	328	8	m	m	PROPN
ejpam-2347	328	9	p	p	PROPN
ejpam-2347	328	10	�	�	PROPN
ejpam-2347	328	11	−	−	PROPN
ejpam-2347	328	12	�	�	PROPN
ejpam-2347	328	13	m+n	m+n	PROPN
ejpam-2347	329	1	p	p	PROPN
ejpam-2347	330	1	�	�	PROPN
ejpam-2347	331	1	•	•	ADP
ejpam-2347	332	1	if	if	SCONJ
ejpam-2347	332	2	m	m	PROPN
ejpam-2347	332	3	,	,	PUNCT
ejpam-2347	332	4	n	n	PROPN
ejpam-2347	332	5	∈	∈	PROPN
ejpam-2347	332	6	n	n	CCONJ
ejpam-2347	332	7	,	,	PUNCT
ejpam-2347	332	8	then	then	ADV
ejpam-2347	332	9	b(n+	b(n+	X
ejpam-2347	332	10	1	1	NUM
ejpam-2347	332	11	,	,	PUNCT
ejpam-2347	332	12	m+	m+	NOUN
ejpam-2347	332	13	1	1	NUM
ejpam-2347	332	14	)	)	PUNCT
ejpam-2347	332	15	=	=	SYM
ejpam-2347	332	16	bp(n+	bp(n+	PROPN
ejpam-2347	332	17	1	1	NUM
ejpam-2347	332	18	,	,	PUNCT
ejpam-2347	332	19	m+	m+	NOUN
ejpam-2347	332	20	1	1	NUM
ejpam-2347	332	21	)	)	PUNCT
ejpam-2347	332	22	�	�	PROPN
ejpam-2347	332	23	n	n	CCONJ
ejpam-2347	332	24	p	p	PROPN
ejpam-2347	332	25	�	�	PROPN
ejpam-2347	332	26	!	!	PUNCT
ejpam-2347	333	1	�	�	PROPN
ejpam-2347	333	2	m	m	PROPN
ejpam-2347	333	3	p	p	PROPN
ejpam-2347	333	4	�	�	PROPN
ejpam-2347	333	5	!	!	PUNCT
ejpam-2347	334	1	�	�	PROPN
ejpam-2347	334	2	m+n+1	m+n+1	VERB
ejpam-2347	334	3	p	p	PROPN
ejpam-2347	334	4	�	�	PROPN
ejpam-2347	334	5	!	!	PUNCT
ejpam-2347	335	1	p	p	PRON
ejpam-2347	335	2	�	�	PROPN
ejpam-2347	335	3	n	n	CCONJ
ejpam-2347	335	4	p	p	PROPN
ejpam-2347	335	5	�	�	PROPN
ejpam-2347	335	6	+	+	CCONJ
ejpam-2347	335	7	�	�	PROPN
ejpam-2347	335	8	m	m	PROPN
ejpam-2347	335	9	p	p	PROPN
ejpam-2347	335	10	�	�	PROPN
ejpam-2347	335	11	−	−	PROPN
ejpam-2347	335	12	�	�	PROPN
ejpam-2347	335	13	m+n+1	m+n+1	VERB
ejpam-2347	335	14	p	p	X
ejpam-2347	335	15	�	�	PROPN
ejpam-2347	335	16	•	•	ADP
ejpam-2347	335	17	if	if	SCONJ
ejpam-2347	335	18	m	m	PROPN
ejpam-2347	335	19	,	,	PUNCT
ejpam-2347	335	20	n	n	PROPN
ejpam-2347	335	21	∈	∈	PROPN
ejpam-2347	335	22	n	n	CCONJ
ejpam-2347	335	23	,	,	PUNCT
ejpam-2347	335	24	then	then	ADV
ejpam-2347	335	25	b(pn	b(pn	PROPN
ejpam-2347	335	26	+	+	CCONJ
ejpam-2347	335	27	1	1	NUM
ejpam-2347	335	28	,	,	PUNCT
ejpam-2347	335	29	pm	pm	NOUN
ejpam-2347	335	30	+	+	NOUN
ejpam-2347	335	31	1	1	X
ejpam-2347	335	32	)	)	PUNCT
ejpam-2347	335	33	=	=	SYM
ejpam-2347	335	34	bp(p	bp(p	NOUN
ejpam-2347	335	35	n	n	CCONJ
ejpam-2347	335	36	,	,	PUNCT
ejpam-2347	335	37	pm	pm	NOUN
ejpam-2347	335	38	)	)	PUNCT
ejpam-2347	335	39	(	(	PUNCT
ejpam-2347	335	40	pn−1)!(pm−1	pn−1)!(pm−1	PROPN
ejpam-2347	335	41	)	)	PUNCT
ejpam-2347	335	42	!	!	PUNCT
ejpam-2347	336	1	(	(	PUNCT
ejpam-2347	336	2	pn−1	pn−1	PROPN
ejpam-2347	336	3	+	+	CCONJ
ejpam-2347	336	4	pm−1	pm−1	NOUN
ejpam-2347	336	5	)	)	PUNCT
ejpam-2347	336	6	!	!	PUNCT
ejpam-2347	337	1	1	1	NUM
ejpam-2347	337	2	hp(p	hp(p	NUM
ejpam-2347	337	3	n	n	PRON
ejpam-2347	337	4	+	+	NOUN
ejpam-2347	337	5	pm)(pn	pm)(pn	PROPN
ejpam-2347	337	6	+	+	NUM
ejpam-2347	337	7	pm	pm	NOUN
ejpam-2347	337	8	+	+	NOUN
ejpam-2347	337	9	1	1	NUM
ejpam-2347	337	10	)	)	PUNCT
ejpam-2347	337	11	•	•	NOUN
ejpam-2347	337	12	if	if	SCONJ
ejpam-2347	337	13	p	p	PROPN
ejpam-2347	337	14	6=	6=	NUM
ejpam-2347	337	15	2	2	NUM
ejpam-2347	337	16	,	,	PUNCT
ejpam-2347	337	17	then	then	ADV
ejpam-2347	337	18	bp	bp	PROPN
ejpam-2347	337	19	(	(	PUNCT
ejpam-2347	337	20	1	1	NUM
ejpam-2347	337	21	2	2	NUM
ejpam-2347	337	22	,	,	PUNCT
ejpam-2347	337	23	1	1	NUM
ejpam-2347	337	24	2	2	NUM
ejpam-2347	337	25	)	)	PUNCT
ejpam-2347	337	26	=	=	PUNCT
ejpam-2347	338	1	¨	¨	NOUN
ejpam-2347	338	2	−1	−1	NOUN
ejpam-2347	338	3	if	if	SCONJ
ejpam-2347	338	4	p	p	PRON
ejpam-2347	338	5	≡	≡	PROPN
ejpam-2347	338	6	3	3	NUM
ejpam-2347	338	7	(	(	PUNCT
ejpam-2347	338	8	mod	mod	NOUN
ejpam-2347	338	9	4	4	NUM
ejpam-2347	338	10	)	)	PUNCT
ejpam-2347	338	11	1	1	NUM
ejpam-2347	338	12	if	if	SCONJ
ejpam-2347	338	13	p	p	PRON
ejpam-2347	338	14	≡	≡	PROPN
ejpam-2347	338	15	1	1	NUM
ejpam-2347	338	16	(	(	PUNCT
ejpam-2347	338	17	mod	mod	NOUN
ejpam-2347	338	18	4	4	NUM
ejpam-2347	338	19	)	)	PUNCT
ejpam-2347	338	20	•	•	NOUN
ejpam-2347	338	21	if	if	SCONJ
ejpam-2347	338	22	m	m	PROPN
ejpam-2347	338	23	,	,	PUNCT
ejpam-2347	338	24	n	n	PROPN
ejpam-2347	338	25	∈	∈	PROPN
ejpam-2347	338	26	n	n	CCONJ
ejpam-2347	338	27	,	,	PUNCT
ejpam-2347	338	28	then	then	ADV
ejpam-2347	338	29	bp(−n,−m	bp(−n,−m	PROPN
ejpam-2347	338	30	)	)	PUNCT
ejpam-2347	338	31	=	=	SYM
ejpam-2347	338	32	(	(	PUNCT
ejpam-2347	338	33	−1	−1	NOUN
ejpam-2347	338	34	)	)	PUNCT
ejpam-2347	338	35	�	�	PROPN
ejpam-2347	338	36	1	1	NUM
ejpam-2347	338	37	+	+	NUM
ejpam-2347	338	38	�	�	PROPN
ejpam-2347	338	39	n+m	n+m	NUM
ejpam-2347	338	40	p	p	PROPN
ejpam-2347	338	41	�	�	PROPN
ejpam-2347	338	42	−	−	PROPN
ejpam-2347	338	43	�	�	PROPN
ejpam-2347	338	44	n	n	CCONJ
ejpam-2347	338	45	p	p	PROPN
ejpam-2347	338	46	�	�	PROPN
ejpam-2347	338	47	−	−	PROPN
ejpam-2347	338	48	�	�	PROPN
ejpam-2347	338	49	m	m	PROPN
ejpam-2347	338	50	p	p	PROPN
ejpam-2347	338	51	�	�	PROPN
ejpam-2347	338	52	�	�	PROPN
ejpam-2347	338	53	hp(n+m	hp(n+m	PROPN
ejpam-2347	338	54	)	)	PUNCT
ejpam-2347	338	55	hp(n)hp(m	hp(n)hp(m	X
ejpam-2347	338	56	)	)	PUNCT
ejpam-2347	338	57	1	1	NUM
ejpam-2347	338	58	bp(n	bp(n	X
ejpam-2347	338	59	,	,	PUNCT
ejpam-2347	338	60	m	m	NOUN
ejpam-2347	338	61	)	)	PUNCT
ejpam-2347	338	62	•	•	ADV
ejpam-2347	338	63	if	if	SCONJ
ejpam-2347	338	64	m	m	PROPN
ejpam-2347	338	65	,	,	PUNCT
ejpam-2347	338	66	n	n	PROPN
ejpam-2347	338	67	∈	∈	PROPN
ejpam-2347	338	68	n	n	CCONJ
ejpam-2347	338	69	,	,	PUNCT
ejpam-2347	338	70	then	then	ADV
ejpam-2347	338	71	bp(−n	bp(−n	ADJ
ejpam-2347	338	72	,	,	PUNCT
ejpam-2347	338	73	m	m	NOUN
ejpam-2347	338	74	)	)	PUNCT
ejpam-2347	338	75	=	=	PUNCT
ejpam-2347	339	1			PROPN
ejpam-2347	339	2			PROPN
ejpam-2347	339	3			PROPN
ejpam-2347	339	4	(	(	PUNCT
ejpam-2347	339	5	−1)m−	−1)m−	X
ejpam-2347	339	6	�	�	PROPN
ejpam-2347	339	7	n	n	CCONJ
ejpam-2347	339	8	p	p	PROPN
ejpam-2347	339	9	�	�	PROPN
ejpam-2347	339	10	+	+	CCONJ
ejpam-2347	339	11	�	�	PROPN
ejpam-2347	339	12	−m+n	−m+n	PROPN
ejpam-2347	339	13	p	p	PROPN
ejpam-2347	339	14	�	�	PROPN
ejpam-2347	339	15	hp(n−m	hp(n−m	NOUN
ejpam-2347	339	16	)	)	PUNCT
ejpam-2347	339	17	hp(n	hp(n	X
ejpam-2347	339	18	)	)	PUNCT
ejpam-2347	339	19	bp(n−m	bp(n−m	PROPN
ejpam-2347	339	20	,	,	PUNCT
ejpam-2347	339	21	m	m	PROPN
ejpam-2347	339	22	)	)	PUNCT
ejpam-2347	339	23	if	if	SCONJ
ejpam-2347	339	24	m	m	VERB
ejpam-2347	339	25	<	<	X
ejpam-2347	339	26	n	n	X
ejpam-2347	339	27	(	(	PUNCT
ejpam-2347	339	28	−1)n+1−	−1)n+1−	PROPN
ejpam-2347	339	29	�	�	PROPN
ejpam-2347	339	30	n	n	CCONJ
ejpam-2347	339	31	p	p	PROPN
ejpam-2347	339	32	�	�	PROPN
ejpam-2347	339	33	1	1	NUM
ejpam-2347	339	34	hp(n	hp(n	NUM
ejpam-2347	339	35	)	)	PUNCT
ejpam-2347	339	36	(	(	PUNCT
ejpam-2347	339	37	bp(m−	bp(m−	PROPN
ejpam-2347	339	38	n	n	CCONJ
ejpam-2347	339	39	,	,	PUNCT
ejpam-2347	339	40	n))−1	n))−1	NOUN
ejpam-2347	339	41	if	if	SCONJ
ejpam-2347	339	42	n≤	n≤	INTJ
ejpam-2347	339	43	m	m	VERB
ejpam-2347	339	44	•	•	ADJ
ejpam-2347	339	45	if	if	SCONJ
ejpam-2347	339	46	m	m	PROPN
ejpam-2347	339	47	,	,	PUNCT
ejpam-2347	339	48	n	n	PROPN
ejpam-2347	339	49	∈	∈	PROPN
ejpam-2347	339	50	n	n	CCONJ
ejpam-2347	339	51	,	,	PUNCT
ejpam-2347	339	52	then	then	ADV
ejpam-2347	339	53	bp(n,−m	bp(n,−m	NOUN
ejpam-2347	339	54	)	)	PUNCT
ejpam-2347	339	55	=	=	PUNCT
ejpam-2347	339	56			PROPN
ejpam-2347	339	57			VERB
ejpam-2347	339	58			PRON
ejpam-2347	339	59			ADJ
ejpam-2347	339	60			PROPN
ejpam-2347	339	61	(	(	PUNCT
ejpam-2347	339	62	−1)m+1−[m	−1)m+1−[m	X
ejpam-2347	339	63	p	p	X
ejpam-2347	339	64	]	]	X
ejpam-2347	339	65	hp(m	hp(m	X
ejpam-2347	339	66	)	)	PUNCT
ejpam-2347	339	67	bp(n−m	bp(n−m	PROPN
ejpam-2347	339	68	,	,	PUNCT
ejpam-2347	339	69	m)−1	m)−1	NOUN
ejpam-2347	339	70	if	if	SCONJ
ejpam-2347	339	71	m≤	m≤	PROPN
ejpam-2347	339	72	n	n	INTJ
ejpam-2347	339	73	(	(	PUNCT
ejpam-2347	339	74	−1)n−	−1)n−	X
ejpam-2347	339	75	[	[	PUNCT
ejpam-2347	339	76	m	m	NOUN
ejpam-2347	339	77	p	p	X
ejpam-2347	339	78	]	]	X
ejpam-2347	340	1	+	+	PROPN
ejpam-2347	340	2	[	[	X
ejpam-2347	340	3	m−n	m−n	NOUN
ejpam-2347	340	4	p	p	X
ejpam-2347	340	5	]	]	X
ejpam-2347	340	6	hp(m−n	hp(m−n	PROPN
ejpam-2347	340	7	)	)	PUNCT
ejpam-2347	340	8	hp(m	hp(m	X
ejpam-2347	340	9	)	)	PUNCT
ejpam-2347	340	10	bp(m−	bp(m−	PROPN
ejpam-2347	340	11	n	n	CCONJ
ejpam-2347	340	12	,	,	PUNCT
ejpam-2347	340	13	n	n	CCONJ
ejpam-2347	340	14	)	)	PUNCT
ejpam-2347	340	15	if	if	SCONJ
ejpam-2347	340	16	n	n	CCONJ
ejpam-2347	340	17	<	<	X
ejpam-2347	340	18	m	m	VERB
ejpam-2347	340	19	acknowledgements	acknowledgement	NOUN
ejpam-2347	340	20	this	this	DET
ejpam-2347	340	21	work	work	NOUN
ejpam-2347	340	22	is	be	AUX
ejpam-2347	340	23	supported	support	VERB
ejpam-2347	340	24	by	by	ADP
ejpam-2347	340	25	mersin	mersin	PROPN
ejpam-2347	340	26	university	university	PROPN
ejpam-2347	340	27	.	.	PUNCT
ejpam-2347	341	1	the	the	DET
ejpam-2347	341	2	authors	author	NOUN
ejpam-2347	341	3	would	would	AUX
ejpam-2347	341	4	like	like	VERB
ejpam-2347	341	5	to	to	PART
ejpam-2347	341	6	thank	thank	VERB
ejpam-2347	341	7	the	the	DET
ejpam-2347	341	8	reviewers	reviewer	NOUN
ejpam-2347	341	9	for	for	ADP
ejpam-2347	341	10	their	their	PRON
ejpam-2347	341	11	useful	useful	ADJ
ejpam-2347	341	12	suggestions	suggestion	NOUN
ejpam-2347	341	13	.	.	PUNCT
ejpam-2347	342	1	references	reference	NOUN
ejpam-2347	342	2	231	231	NUM
ejpam-2347	342	3	references	reference	NOUN
ejpam-2347	342	4	[	[	X
ejpam-2347	342	5	1	1	NUM
ejpam-2347	342	6	]	]	PUNCT
ejpam-2347	342	7	l.	l.	PROPN
ejpam-2347	342	8	c.	c.	PROPN
ejpam-2347	342	9	andrews	andrews	PROPN
ejpam-2347	342	10	.	.	PUNCT
ejpam-2347	343	1	special	special	ADJ
ejpam-2347	343	2	functions	function	NOUN
ejpam-2347	343	3	for	for	ADP
ejpam-2347	343	4	engineer	engineer	NOUN
ejpam-2347	343	5	and	and	CCONJ
ejpam-2347	343	6	applied	apply	VERB
ejpam-2347	343	7	mathematicians	mathematician	NOUN
ejpam-2347	343	8	,	,	PUNCT
ejpam-2347	343	9	macmillan	macmillan	PROPN
ejpam-2347	343	10	publishing	publishing	PROPN
ejpam-2347	343	11	company	company	PROPN
ejpam-2347	343	12	,	,	PUNCT
ejpam-2347	343	13	london	london	PROPN
ejpam-2347	343	14	,	,	PUNCT
ejpam-2347	343	15	1985	1985	NUM
ejpam-2347	343	16	.	.	PUNCT
ejpam-2347	344	1	[	[	X
ejpam-2347	344	2	2	2	NUM
ejpam-2347	344	3	]	]	PUNCT
ejpam-2347	344	4	f.	f.	NOUN
ejpam-2347	344	5	baldassarri	baldassarri	PROPN
ejpam-2347	344	6	.	.	PUNCT
ejpam-2347	345	1	etale	etale	NOUN
ejpam-2347	345	2	and	and	CCONJ
ejpam-2347	345	3	crystalline	crystalline	ADJ
ejpam-2347	345	4	beta	beta	NOUN
ejpam-2347	345	5	and	and	CCONJ
ejpam-2347	345	6	gamma	gamma	NOUN
ejpam-2347	345	7	functions	function	NOUN
ejpam-2347	345	8	via	via	ADP
ejpam-2347	345	9	fontaine	fontaine	PROPN
ejpam-2347	345	10	’s	’s	PART
ejpam-2347	345	11	periods	period	NOUN
ejpam-2347	345	12	,	,	PUNCT
ejpam-2347	345	13	atti	atti	PROPN
ejpam-2347	345	14	della	della	PROPN
ejpam-2347	345	15	accademia	accademia	PROPN
ejpam-2347	345	16	nazionale	nazionale	PROPN
ejpam-2347	345	17	dei	dei	PROPN
ejpam-2347	345	18	lincei	lincei	NOUN
ejpam-2347	345	19	.	.	PUNCT
ejpam-2347	346	1	rendiconti	rendiconti	ADJ
ejpam-2347	346	2	lincei	lincei	NOUN
ejpam-2347	346	3	.	.	PUNCT
ejpam-2347	347	1	matematicae	matematicae	PROPN
ejpam-2347	347	2	applicazioni	applicazioni	PROPN
ejpam-2347	347	3	(	(	PUNCT
ejpam-2347	347	4	9	9	NUM
ejpam-2347	347	5	)	)	PUNCT
ejpam-2347	347	6	,	,	PUNCT
ejpam-2347	347	7	17(2	17(2	NUM
ejpam-2347	347	8	)	)	PUNCT
ejpam-2347	347	9	,	,	PUNCT
ejpam-2347	347	10	175	175	NUM
ejpam-2347	347	11	-	-	SYM
ejpam-2347	347	12	198	198	NUM
ejpam-2347	347	13	.	.	PUNCT
ejpam-2347	347	14	2006	2006	NUM
ejpam-2347	347	15	.	.	PUNCT
ejpam-2347	348	1	[	[	X
ejpam-2347	348	2	3	3	X
ejpam-2347	348	3	]	]	X
ejpam-2347	348	4	d.	d.	PROPN
ejpam-2347	348	5	barsky	barsky	PROPN
ejpam-2347	348	6	.	.	PUNCT
ejpam-2347	349	1	on	on	ADP
ejpam-2347	349	2	morita	morita	PROPN
ejpam-2347	349	3	’s	’s	PART
ejpam-2347	349	4	p	p	ADJ
ejpam-2347	349	5	-	-	PUNCT
ejpam-2347	349	6	adic	adic	ADJ
ejpam-2347	349	7	gamma	gamma	NOUN
ejpam-2347	349	8	function	function	NOUN
ejpam-2347	349	9	,	,	PUNCT
ejpam-2347	349	10	mathematical	mathematical	ADJ
ejpam-2347	349	11	proceedings	proceeding	NOUN
ejpam-2347	349	12	of	of	ADP
ejpam-2347	349	13	the	the	DET
ejpam-2347	349	14	cambridge	cambridge	PROPN
ejpam-2347	349	15	philosophical	philosophical	ADJ
ejpam-2347	349	16	society	society	NOUN
ejpam-2347	349	17	,	,	PUNCT
ejpam-2347	349	18	89(1	89(1	NOUN
ejpam-2347	349	19	)	)	PUNCT
ejpam-2347	349	20	,	,	PUNCT
ejpam-2347	349	21	23	23	NUM
ejpam-2347	349	22	-	-	SYM
ejpam-2347	349	23	27	27	NUM
ejpam-2347	349	24	.	.	PUNCT
ejpam-2347	349	25	1981	1981	NUM
ejpam-2347	349	26	.	.	PUNCT
ejpam-2347	350	1	[	[	X
ejpam-2347	350	2	4	4	NUM
ejpam-2347	350	3	]	]	PUNCT
ejpam-2347	350	4	m.	m.	NOUN
ejpam-2347	350	5	boyarsky	boyarsky	NOUN
ejpam-2347	350	6	.	.	PUNCT
ejpam-2347	351	1	p	p	X
ejpam-2347	351	2	-	-	PUNCT
ejpam-2347	351	3	adic	adic	ADJ
ejpam-2347	351	4	gamma	gamma	NOUN
ejpam-2347	351	5	functions	function	NOUN
ejpam-2347	351	6	and	and	CCONJ
ejpam-2347	351	7	dwork	dwork	ADJ
ejpam-2347	351	8	cohomology	cohomology	NOUN
ejpam-2347	351	9	,	,	PUNCT
ejpam-2347	351	10	transactions	transaction	NOUN
ejpam-2347	351	11	of	of	ADP
ejpam-2347	351	12	the	the	DET
ejpam-2347	351	13	american	american	PROPN
ejpam-2347	351	14	mathematical	mathematical	PROPN
ejpam-2347	351	15	society	society	NOUN
ejpam-2347	351	16	,	,	PUNCT
ejpam-2347	351	17	257(2	257(2	NUM
ejpam-2347	351	18	)	)	PUNCT
ejpam-2347	351	19	,	,	PUNCT
ejpam-2347	351	20	359	359	NUM
ejpam-2347	351	21	-	-	SYM
ejpam-2347	351	22	369	369	NUM
ejpam-2347	351	23	.	.	PUNCT
ejpam-2347	351	24	1980	1980	NUM
ejpam-2347	351	25	.	.	PUNCT
ejpam-2347	352	1	[	[	X
ejpam-2347	352	2	5	5	X
ejpam-2347	352	3	]	]	PUNCT
ejpam-2347	352	4	h.	h.	PROPN
ejpam-2347	352	5	cohen	cohen	PROPN
ejpam-2347	352	6	and	and	CCONJ
ejpam-2347	352	7	e.	e.	PROPN
ejpam-2347	352	8	friedman	friedman	PROPN
ejpam-2347	352	9	.	.	PUNCT
ejpam-2347	353	1	raabe	raabe	PROPN
ejpam-2347	353	2	’s	’s	PART
ejpam-2347	353	3	formula	formula	NOUN
ejpam-2347	353	4	for	for	ADP
ejpam-2347	353	5	p	p	NOUN
ejpam-2347	353	6	-	-	PUNCT
ejpam-2347	353	7	adic	adic	ADJ
ejpam-2347	353	8	gamma	gamma	NOUN
ejpam-2347	353	9	and	and	CCONJ
ejpam-2347	353	10	zeta	zeta	PROPN
ejpam-2347	353	11	functions	function	NOUN
ejpam-2347	353	12	,	,	PUNCT
ejpam-2347	353	13	universitãl	universitãl	NOUN
ejpam-2347	353	14	’	'	PUNCT
ejpam-2347	353	15	de	de	X
ejpam-2347	353	16	grenoble	grenoble	X
ejpam-2347	353	17	.	.	PUNCT
ejpam-2347	354	1	annales	annales	PROPN
ejpam-2347	354	2	de	de	PROPN
ejpam-2347	354	3	l’institut	l’institut	PROPN
ejpam-2347	354	4	fourier	fourier	NOUN
ejpam-2347	354	5	,	,	PUNCT
ejpam-2347	354	6	58(1	58(1	NUM
ejpam-2347	354	7	)	)	PUNCT
ejpam-2347	354	8	,	,	PUNCT
ejpam-2347	354	9	363	363	NUM
ejpam-2347	354	10	-	-	SYM
ejpam-2347	354	11	376	376	NUM
ejpam-2347	354	12	.	.	PUNCT
ejpam-2347	354	13	2008	2008	NUM
ejpam-2347	354	14	.	.	PUNCT
ejpam-2347	355	1	[	[	X
ejpam-2347	355	2	6	6	X
ejpam-2347	355	3	]	]	PUNCT
ejpam-2347	355	4	j.	j.	PROPN
ejpam-2347	355	5	diamond	diamond	PROPN
ejpam-2347	355	6	.	.	PUNCT
ejpam-2347	356	1	the	the	DET
ejpam-2347	356	2	p	p	NOUN
ejpam-2347	356	3	-	-	PUNCT
ejpam-2347	356	4	adic	adic	ADJ
ejpam-2347	356	5	log	log	NOUN
ejpam-2347	356	6	gamma	gamma	NOUN
ejpam-2347	356	7	function	function	NOUN
ejpam-2347	356	8	and	and	CCONJ
ejpam-2347	356	9	p	p	NOUN
ejpam-2347	356	10	-	-	PUNCT
ejpam-2347	356	11	adic	adic	PROPN
ejpam-2347	356	12	euler	euler	NOUN
ejpam-2347	356	13	constant	constant	ADJ
ejpam-2347	356	14	,	,	PUNCT
ejpam-2347	356	15	transactions	transaction	NOUN
ejpam-2347	356	16	of	of	ADP
ejpam-2347	356	17	the	the	DET
ejpam-2347	356	18	american	american	PROPN
ejpam-2347	356	19	mathematical	mathematical	PROPN
ejpam-2347	356	20	society	society	NOUN
ejpam-2347	356	21	,	,	PUNCT
ejpam-2347	356	22	233	233	NUM
ejpam-2347	356	23	,	,	PUNCT
ejpam-2347	356	24	321	321	NUM
ejpam-2347	356	25	-	-	SYM
ejpam-2347	356	26	337	337	NUM
ejpam-2347	356	27	.	.	PUNCT
ejpam-2347	356	28	1977	1977	NUM
ejpam-2347	356	29	.	.	PUNCT
ejpam-2347	357	1	[	[	X
ejpam-2347	357	2	7	7	X
ejpam-2347	357	3	]	]	X
ejpam-2347	357	4	b.	b.	PROPN
ejpam-2347	357	5	dwork	dwork	PROPN
ejpam-2347	357	6	.	.	PUNCT
ejpam-2347	358	1	a	a	DET
ejpam-2347	358	2	note	note	NOUN
ejpam-2347	358	3	on	on	ADP
ejpam-2347	358	4	p	p	ADJ
ejpam-2347	358	5	-	-	PUNCT
ejpam-2347	358	6	adic	adic	ADJ
ejpam-2347	358	7	gamma	gamma	NOUN
ejpam-2347	358	8	function	function	NOUN
ejpam-2347	358	9	,	,	PUNCT
ejpam-2347	358	10	study	study	NOUN
ejpam-2347	358	11	group	group	NOUN
ejpam-2347	358	12	on	on	ADP
ejpam-2347	358	13	ultrametric	ultrametric	ADJ
ejpam-2347	358	14	analysis	analysis	NOUN
ejpam-2347	358	15	,	,	PUNCT
ejpam-2347	358	16	9th	9th	ADJ
ejpam-2347	358	17	year	year	NOUN
ejpam-2347	358	18	:	:	PUNCT
ejpam-2347	358	19	1981/82	1981/82	NUM
ejpam-2347	358	20	,	,	PUNCT
ejpam-2347	358	21	no	no	INTJ
ejpam-2347	358	22	.	.	NOUN
ejpam-2347	358	23	3	3	NUM
ejpam-2347	358	24	(	(	PUNCT
ejpam-2347	358	25	marseille	marseille	NOUN
ejpam-2347	358	26	,	,	PUNCT
ejpam-2347	358	27	1982	1982	NUM
ejpam-2347	358	28	)	)	PUNCT
ejpam-2347	358	29	,	,	PUNCT
ejpam-2347	358	30	exp	exp	NOUN
ejpam-2347	358	31	.	.	PUNCT
ejpam-2347	359	1	no	no	INTJ
ejpam-2347	359	2	.	.	PUNCT
ejpam-2347	360	1	j5	j5	PROPN
ejpam-2347	360	2	,	,	PUNCT
ejpam-2347	360	3	10	10	NUM
ejpam-2347	360	4	pp	pp	NOUN
ejpam-2347	360	5	.	.	PUNCT
ejpam-2347	360	6	,	,	PUNCT
ejpam-2347	360	7	inst	inst	PROPN
ejpam-2347	360	8	.	.	PUNCT
ejpam-2347	361	1	henri	henri	PROPN
ejpam-2347	361	2	poincaré	poincaré	PROPN
ejpam-2347	361	3	,	,	PUNCT
ejpam-2347	361	4	paris	paris	PROPN
ejpam-2347	361	5	,	,	PUNCT
ejpam-2347	361	6	1983	1983	NUM
ejpam-2347	361	7	.	.	PUNCT
ejpam-2347	362	1	[	[	X
ejpam-2347	362	2	8	8	NUM
ejpam-2347	362	3	]	]	X
ejpam-2347	362	4	b.	b.	PROPN
ejpam-2347	362	5	h.	h.	PROPN
ejpam-2347	362	6	gross	gross	PROPN
ejpam-2347	362	7	and	and	CCONJ
ejpam-2347	362	8	n.	n.	PROPN
ejpam-2347	362	9	koblitz	koblitz	PROPN
ejpam-2347	362	10	.	.	PUNCT
ejpam-2347	363	1	gauss	gauss	ADJ
ejpam-2347	363	2	sums	sum	NOUN
ejpam-2347	363	3	and	and	CCONJ
ejpam-2347	363	4	the	the	DET
ejpam-2347	363	5	p	p	NOUN
ejpam-2347	363	6	-	-	PUNCT
ejpam-2347	363	7	adic	adic	ADJ
ejpam-2347	363	8	γ	γ	NOUN
ejpam-2347	363	9	-	-	NOUN
ejpam-2347	363	10	function	function	NOUN
ejpam-2347	363	11	,	,	PUNCT
ejpam-2347	363	12	the	the	DET
ejpam-2347	363	13	annals	annal	NOUN
ejpam-2347	363	14	of	of	ADP
ejpam-2347	363	15	mathematics	mathematic	NOUN
ejpam-2347	363	16	,	,	PUNCT
ejpam-2347	363	17	second	second	ADJ
ejpam-2347	363	18	series	series	NOUN
ejpam-2347	363	19	,	,	PUNCT
ejpam-2347	363	20	109(3	109(3	NUM
ejpam-2347	363	21	)	)	PUNCT
ejpam-2347	363	22	,	,	PUNCT
ejpam-2347	363	23	569	569	NUM
ejpam-2347	363	24	-	-	SYM
ejpam-2347	363	25	581	581	NUM
ejpam-2347	363	26	.	.	PUNCT
ejpam-2347	363	27	1979	1979	NUM
ejpam-2347	363	28	.	.	PUNCT
ejpam-2347	364	1	[	[	X
ejpam-2347	364	2	9	9	NUM
ejpam-2347	364	3	]	]	PUNCT
ejpam-2347	364	4	t.	t.	PROPN
ejpam-2347	364	5	k.	k.	PROPN
ejpam-2347	364	6	kim	kim	PROPN
ejpam-2347	364	7	.	.	PUNCT
ejpam-2347	365	1	a	a	DET
ejpam-2347	365	2	note	note	NOUN
ejpam-2347	365	3	on	on	ADP
ejpam-2347	365	4	analogue	analogue	NOUN
ejpam-2347	365	5	of	of	ADP
ejpam-2347	365	6	gamma	gamma	NOUN
ejpam-2347	365	7	functions	function	NOUN
ejpam-2347	365	8	,	,	PUNCT
ejpam-2347	365	9	in	in	ADP
ejpam-2347	365	10	proceedings	proceeding	NOUN
ejpam-2347	365	11	of	of	ADP
ejpam-2347	365	12	the	the	DET
ejpam-2347	365	13	5th	5th	ADJ
ejpam-2347	365	14	transcendental	transcendental	ADJ
ejpam-2347	365	15	number	number	NOUN
ejpam-2347	365	16	theory	theory	NOUN
ejpam-2347	365	17	,	,	PUNCT
ejpam-2347	365	18	111–118	111–118	NUM
ejpam-2347	365	19	,	,	PUNCT
ejpam-2347	365	20	gakushin	gakushin	PROPN
ejpam-2347	365	21	university	university	PROPN
ejpam-2347	365	22	,	,	PUNCT
ejpam-2347	365	23	tokyo	tokyo	PROPN
ejpam-2347	365	24	,	,	PUNCT
ejpam-2347	365	25	japan	japan	PROPN
ejpam-2347	365	26	,	,	PUNCT
ejpam-2347	365	27	1997	1997	NUM
ejpam-2347	365	28	.	.	PUNCT
ejpam-2347	366	1	[	[	X
ejpam-2347	366	2	10	10	NUM
ejpam-2347	366	3	]	]	X
ejpam-2347	366	4	y.	y.	PROPN
ejpam-2347	366	5	morita	morita	PROPN
ejpam-2347	366	6	.	.	PUNCT
ejpam-2347	367	1	a	a	DET
ejpam-2347	367	2	p	p	ADJ
ejpam-2347	367	3	-	-	PUNCT
ejpam-2347	367	4	adic	adic	ADJ
ejpam-2347	367	5	analogue	analogue	NOUN
ejpam-2347	367	6	of	of	ADP
ejpam-2347	367	7	the	the	DET
ejpam-2347	367	8	γ	γ	NOUN
ejpam-2347	367	9	-	-	NOUN
ejpam-2347	367	10	function	function	NOUN
ejpam-2347	367	11	,	,	PUNCT
ejpam-2347	367	12	journal	journal	NOUN
ejpam-2347	367	13	of	of	ADP
ejpam-2347	367	14	the	the	DET
ejpam-2347	367	15	faculty	faculty	NOUN
ejpam-2347	367	16	of	of	ADP
ejpam-2347	367	17	science	science	NOUN
ejpam-2347	367	18	.	.	PUNCT
ejpam-2347	368	1	university	university	NOUN
ejpam-2347	368	2	of	of	ADP
ejpam-2347	368	3	tokyo	tokyo	PROPN
ejpam-2347	368	4	.	.	PUNCT
ejpam-2347	369	1	section	section	PROPN
ejpam-2347	369	2	ia	ia	PROPN
ejpam-2347	369	3	.	.	PROPN
ejpam-2347	369	4	mathematics	mathematics	PROPN
ejpam-2347	369	5	,	,	PUNCT
ejpam-2347	369	6	22	22	NUM
ejpam-2347	369	7	,	,	PUNCT
ejpam-2347	369	8	225	225	NUM
ejpam-2347	369	9	-	-	SYM
ejpam-2347	369	10	266	266	NUM
ejpam-2347	369	11	.	.	PUNCT
ejpam-2347	369	12	1975	1975	NUM
ejpam-2347	369	13	.	.	PUNCT
ejpam-2347	370	1	[	[	X
ejpam-2347	370	2	11	11	NUM
ejpam-2347	370	3	]	]	X
ejpam-2347	370	4	g.	g.	PROPN
ejpam-2347	370	5	overholtzer	overholtzer	PROPN
ejpam-2347	370	6	.	.	PUNCT
ejpam-2347	371	1	sum	sum	NOUN
ejpam-2347	371	2	functions	function	NOUN
ejpam-2347	371	3	in	in	ADP
ejpam-2347	371	4	elementary	elementary	ADJ
ejpam-2347	371	5	p	p	PROPN
ejpam-2347	371	6	-	-	PUNCT
ejpam-2347	371	7	adic	adic	ADJ
ejpam-2347	371	8	analysis	analysis	NOUN
ejpam-2347	371	9	,	,	PUNCT
ejpam-2347	371	10	american	american	ADJ
ejpam-2347	371	11	journal	journal	NOUN
ejpam-2347	371	12	of	of	ADP
ejpam-2347	371	13	mathematics	mathematic	NOUN
ejpam-2347	371	14	,	,	PUNCT
ejpam-2347	371	15	74	74	NUM
ejpam-2347	371	16	,	,	PUNCT
ejpam-2347	371	17	332	332	NUM
ejpam-2347	371	18	-	-	SYM
ejpam-2347	371	19	346	346	NUM
ejpam-2347	371	20	.	.	PUNCT
ejpam-2347	371	21	1952	1952	NUM
ejpam-2347	371	22	.	.	PUNCT
ejpam-2347	372	1	[	[	X
ejpam-2347	372	2	12	12	NUM
ejpam-2347	372	3	]	]	PUNCT
ejpam-2347	372	4	w.	w.	PROPN
ejpam-2347	372	5	h.	h.	PROPN
ejpam-2347	372	6	schikhof	schikhof	PROPN
ejpam-2347	372	7	.	.	PUNCT
ejpam-2347	373	1	ultrametric	ultrametric	ADJ
ejpam-2347	373	2	calculus	calculus	NOUN
ejpam-2347	373	3	:	:	PUNCT
ejpam-2347	373	4	an	an	DET
ejpam-2347	373	5	introduction	introduction	NOUN
ejpam-2347	373	6	to	to	ADP
ejpam-2347	373	7	p	p	NOUN
ejpam-2347	373	8	-	-	PUNCT
ejpam-2347	373	9	adic	adic	ADJ
ejpam-2347	373	10	analysis	analysis	NOUN
ejpam-2347	373	11	,	,	PUNCT
ejpam-2347	373	12	cambridge	cambridge	PROPN
ejpam-2347	373	13	university	university	PROPN
ejpam-2347	373	14	press	press	NOUN
ejpam-2347	373	15	,	,	PUNCT
ejpam-2347	373	16	1984	1984	NUM
ejpam-2347	373	17	.	.	PUNCT
ejpam-2347	374	1	[	[	X
ejpam-2347	374	2	13	13	NUM
ejpam-2347	374	3	]	]	X
ejpam-2347	374	4	i.	i.	PROPN
ejpam-2347	374	5	shapiro	shapiro	PROPN
ejpam-2347	374	6	.	.	PUNCT
ejpam-2347	374	7	frobenius	frobenius	PROPN
ejpam-2347	374	8	map	map	NOUN
ejpam-2347	374	9	and	and	CCONJ
ejpam-2347	374	10	the	the	DET
ejpam-2347	374	11	p	p	ADJ
ejpam-2347	374	12	-	-	PUNCT
ejpam-2347	374	13	adic	adic	ADJ
ejpam-2347	374	14	gamma	gamma	NOUN
ejpam-2347	374	15	function	function	NOUN
ejpam-2347	374	16	,	,	PUNCT
ejpam-2347	374	17	journal	journal	NOUN
ejpam-2347	374	18	of	of	ADP
ejpam-2347	374	19	number	number	NOUN
ejpam-2347	374	20	theory	theory	NOUN
ejpam-2347	374	21	,	,	PUNCT
ejpam-2347	374	22	132(8	132(8	NUM
ejpam-2347	374	23	)	)	PUNCT
ejpam-2347	374	24	,	,	PUNCT
ejpam-2347	374	25	1770	1770	NUM
ejpam-2347	374	26	-	-	SYM
ejpam-2347	374	27	1779	1779	NUM
ejpam-2347	374	28	.	.	PUNCT
ejpam-2347	374	29	2012	2012	NUM
ejpam-2347	374	30	.	.	PUNCT