id	sid	tid	token	lemma	pos
ejpam-1854	1	1	european	european	PROPN
ejpam-1854	1	2	journal	journal	PROPN
ejpam-1854	1	3	of	of	ADP
ejpam-1854	1	4	pure	pure	ADJ
ejpam-1854	1	5	and	and	CCONJ
ejpam-1854	1	6	applied	apply	VERB
ejpam-1854	1	7	mathematics	mathematic	NOUN
ejpam-1854	1	8	vol	vol	NOUN
ejpam-1854	1	9	.	.	PROPN
ejpam-1854	2	1	6	6	NUM
ejpam-1854	2	2	,	,	PUNCT
ejpam-1854	2	3	no	no	INTJ
ejpam-1854	2	4	.	.	NOUN
ejpam-1854	2	5	2	2	NUM
ejpam-1854	2	6	,	,	PUNCT
ejpam-1854	2	7	2013	2013	NUM
ejpam-1854	2	8	,	,	PUNCT
ejpam-1854	2	9	239	239	NUM
ejpam-1854	2	10	-	-	SYM
ejpam-1854	2	11	246	246	NUM
ejpam-1854	2	12	issn	issn	PROPN
ejpam-1854	2	13	1307	1307	NUM
ejpam-1854	2	14	-	-	SYM
ejpam-1854	2	15	5543	5543	NUM
ejpam-1854	2	16	–	–	PUNCT
ejpam-1854	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1854	2	18	on	on	ADP
ejpam-1854	2	19	some	some	DET
ejpam-1854	2	20	properties	property	NOUN
ejpam-1854	2	21	of	of	ADP
ejpam-1854	2	22	liouville	liouville	NOUN
ejpam-1854	2	23	numbers	number	NOUN
ejpam-1854	2	24	in	in	ADP
ejpam-1854	2	25	the	the	DET
ejpam-1854	2	26	non	non	ADJ
ejpam-1854	2	27	-	-	ADJ
ejpam-1854	2	28	archimedean	archimedean	ADJ
ejpam-1854	2	29	case	case	NOUN
ejpam-1854	2	30	hamza	hamza	PROPN
ejpam-1854	2	31	menken1,∗	menken1,∗	NOUN
ejpam-1854	2	32	,	,	PUNCT
ejpam-1854	2	33	abdulkadir	abdulkadir	ADJ
ejpam-1854	2	34	aşan2	aşan2	PROPN
ejpam-1854	2	35	1	1	NUM
ejpam-1854	2	36	mersin	mersin	PROPN
ejpam-1854	2	37	university	university	PROPN
ejpam-1854	2	38	,	,	PUNCT
ejpam-1854	2	39	science	science	NOUN
ejpam-1854	2	40	and	and	CCONJ
ejpam-1854	2	41	arts	art	NOUN
ejpam-1854	2	42	faculty	faculty	NOUN
ejpam-1854	2	43	,	,	PUNCT
ejpam-1854	2	44	mathematics	mathematics	PROPN
ejpam-1854	2	45	department	department	PROPN
ejpam-1854	2	46	,	,	PUNCT
ejpam-1854	2	47	mersin	mersin	PROPN
ejpam-1854	2	48	-	-	PUNCT
ejpam-1854	2	49	turkey	turkey	PROPN
ejpam-1854	2	50	2	2	NUM
ejpam-1854	2	51	mersin	mersin	PROPN
ejpam-1854	2	52	university	university	PROPN
ejpam-1854	2	53	,	,	PUNCT
ejpam-1854	2	54	institute	institute	PROPN
ejpam-1854	2	55	of	of	ADP
ejpam-1854	2	56	science	science	PROPN
ejpam-1854	2	57	,	,	PUNCT
ejpam-1854	2	58	mathematics	mathematics	PROPN
ejpam-1854	2	59	graduate	graduate	PROPN
ejpam-1854	2	60	program	program	NOUN
ejpam-1854	2	61	,	,	PUNCT
ejpam-1854	2	62	mersin	mersin	PROPN
ejpam-1854	2	63	-	-	PUNCT
ejpam-1854	2	64	turkey	turkey	PROPN
ejpam-1854	2	65	abstract	abstract	NOUN
ejpam-1854	2	66	.	.	PUNCT
ejpam-1854	3	1	we	we	PRON
ejpam-1854	3	2	study	study	VERB
ejpam-1854	3	3	liouville	liouville	NOUN
ejpam-1854	3	4	numbers	number	NOUN
ejpam-1854	3	5	in	in	ADP
ejpam-1854	3	6	the	the	DET
ejpam-1854	3	7	non	non	ADJ
ejpam-1854	3	8	-	-	ADJ
ejpam-1854	3	9	archimedean	archimedean	ADJ
ejpam-1854	3	10	case	case	NOUN
ejpam-1854	3	11	.	.	PUNCT
ejpam-1854	4	1	we	we	PRON
ejpam-1854	4	2	give	give	VERB
ejpam-1854	4	3	the	the	DET
ejpam-1854	4	4	analogues	analogue	NOUN
ejpam-1854	4	5	of	of	ADP
ejpam-1854	4	6	the	the	DET
ejpam-1854	4	7	erdös	erdös	PROPN
ejpam-1854	4	8	theorem	theorem	NOUN
ejpam-1854	4	9	in	in	ADP
ejpam-1854	4	10	the	the	DET
ejpam-1854	4	11	non	non	ADJ
ejpam-1854	4	12	-	-	ADJ
ejpam-1854	4	13	archimedean	archimedean	ADJ
ejpam-1854	4	14	case	case	NOUN
ejpam-1854	4	15	,	,	PUNCT
ejpam-1854	4	16	both	both	PRON
ejpam-1854	4	17	in	in	ADP
ejpam-1854	4	18	the	the	DET
ejpam-1854	4	19	p	p	NOUN
ejpam-1854	4	20	-	-	PUNCT
ejpam-1854	4	21	adic	adic	ADJ
ejpam-1854	4	22	numbers	number	NOUN
ejpam-1854	4	23	field	field	VERB
ejpam-1854	4	24	qp	qp	NOUN
ejpam-1854	4	25	and	and	CCONJ
ejpam-1854	4	26	the	the	DET
ejpam-1854	4	27	functions	function	NOUN
ejpam-1854	4	28	field	field	NOUN
ejpam-1854	4	29	k	k	PROPN
ejpam-1854	4	30	〈	〈	PROPN
ejpam-1854	4	31	x	x	X
ejpam-1854	4	32	〉	〉	NOUN
ejpam-1854	4	33	.	.	PUNCT
ejpam-1854	4	34	2010	2010	NUM
ejpam-1854	4	35	mathematics	mathematic	NOUN
ejpam-1854	4	36	subject	subject	NOUN
ejpam-1854	4	37	classifications	classification	NOUN
ejpam-1854	4	38	:	:	PUNCT
ejpam-1854	4	39	11j61	11j61	NUM
ejpam-1854	4	40	,	,	PUNCT
ejpam-1854	4	41	12j25	12j25	NUM
ejpam-1854	4	42	,	,	PUNCT
ejpam-1854	4	43	11r58	11r58	NUM
ejpam-1854	4	44	key	key	ADJ
ejpam-1854	4	45	words	word	NOUN
ejpam-1854	4	46	and	and	CCONJ
ejpam-1854	4	47	phrases	phrase	NOUN
ejpam-1854	4	48	:	:	PUNCT
ejpam-1854	4	49	non	non	ADJ
ejpam-1854	4	50	-	-	ADJ
ejpam-1854	4	51	archimedean	archimedean	ADJ
ejpam-1854	4	52	field	field	NOUN
ejpam-1854	4	53	,	,	PUNCT
ejpam-1854	4	54	p	p	NOUN
ejpam-1854	4	55	-	-	PUNCT
ejpam-1854	4	56	adic	adic	ADJ
ejpam-1854	4	57	number	number	NOUN
ejpam-1854	4	58	,	,	PUNCT
ejpam-1854	4	59	p	p	NOUN
ejpam-1854	4	60	-	-	PUNCT
ejpam-1854	4	61	adic	adic	ADJ
ejpam-1854	4	62	liouville	liouville	NOUN
ejpam-1854	4	63	number	number	NOUN
ejpam-1854	4	64	,	,	PUNCT
ejpam-1854	4	65	functions	function	NOUN
ejpam-1854	4	66	field	field	NOUN
ejpam-1854	4	67	.	.	PUNCT
ejpam-1854	5	1	1	1	X
ejpam-1854	5	2	.	.	X
ejpam-1854	5	3	introduction	introduction	NOUN
ejpam-1854	5	4	the	the	DET
ejpam-1854	5	5	classical	classical	ADJ
ejpam-1854	5	6	liouville	liouville	NOUN
ejpam-1854	5	7	’s	’s	PART
ejpam-1854	5	8	theorem	theorem	ADJ
ejpam-1854	5	9	states	state	NOUN
ejpam-1854	5	10	that	that	SCONJ
ejpam-1854	5	11	if	if	SCONJ
ejpam-1854	5	12	α	α	PRON
ejpam-1854	5	13	∈	∈	NOUN
ejpam-1854	5	14	r	r	NOUN
ejpam-1854	5	15	is	be	AUX
ejpam-1854	5	16	an	an	DET
ejpam-1854	5	17	algebraic	algebraic	ADJ
ejpam-1854	5	18	number	number	NOUN
ejpam-1854	5	19	of	of	ADP
ejpam-1854	5	20	degree	degree	NOUN
ejpam-1854	5	21	n≥	n≥	NOUN
ejpam-1854	5	22	2	2	NUM
ejpam-1854	5	23	,	,	PUNCT
ejpam-1854	5	24	then	then	ADV
ejpam-1854	5	25	there	there	PRON
ejpam-1854	5	26	exists	exist	VERB
ejpam-1854	5	27	a	a	DET
ejpam-1854	5	28	positive	positive	ADJ
ejpam-1854	5	29	constant	constant	ADJ
ejpam-1854	5	30	c(α	c(α	NOUN
ejpam-1854	5	31	)	)	PUNCT
ejpam-1854	5	32	depending	depend	VERB
ejpam-1854	5	33	only	only	ADV
ejpam-1854	5	34	on	on	ADP
ejpam-1854	5	35	α	α	PRON
ejpam-1854	5	36	such	such	ADJ
ejpam-1854	5	37	that	that	SCONJ
ejpam-1854	5	38	�	�	PROPN
ejpam-1854	5	39	�	�	PROPN
ejpam-1854	5	40	�	�	PROPN
ejpam-1854	5	41	α−	α−	ADP
ejpam-1854	5	42	a	a	DET
ejpam-1854	5	43	b	b	PROPN
ejpam-1854	5	44	�	�	PROPN
ejpam-1854	5	45	�	�	PROPN
ejpam-1854	5	46	�	�	PROPN
ejpam-1854	5	47	≥	≥	PROPN
ejpam-1854	5	48	c(α	c(α	NOUN
ejpam-1854	5	49	)	)	PUNCT
ejpam-1854	5	50	bn	bn	ADP
ejpam-1854	5	51	for	for	ADP
ejpam-1854	5	52	all	all	DET
ejpam-1854	5	53	a	a	PRON
ejpam-1854	5	54	,	,	PUNCT
ejpam-1854	5	55	b	b	X
ejpam-1854	5	56	∈	∈	PROPN
ejpam-1854	5	57	z+	z+	PUNCT
ejpam-1854	5	58	.	.	PUNCT
ejpam-1854	6	1	the	the	DET
ejpam-1854	6	2	existence	existence	NOUN
ejpam-1854	6	3	of	of	ADP
ejpam-1854	6	4	transcendental	transcendental	ADJ
ejpam-1854	6	5	numbers	number	NOUN
ejpam-1854	6	6	has	have	AUX
ejpam-1854	6	7	been	be	AUX
ejpam-1854	6	8	usually	usually	ADV
ejpam-1854	6	9	shown	show	VERB
ejpam-1854	6	10	using	use	VERB
ejpam-1854	6	11	the	the	DET
ejpam-1854	6	12	liouville	liouville	NOUN
ejpam-1854	6	13	’s	’s	PART
ejpam-1854	6	14	theorem	theorem	ADJ
ejpam-1854	6	15	.	.	PROPN
ejpam-1854	7	1	for	for	ADP
ejpam-1854	7	2	instance	instance	NOUN
ejpam-1854	7	3	,	,	PUNCT
ejpam-1854	7	4	the	the	DET
ejpam-1854	7	5	transcendence	transcendence	NOUN
ejpam-1854	7	6	of	of	ADP
ejpam-1854	7	7	the	the	DET
ejpam-1854	7	8	number	number	NOUN
ejpam-1854	7	9	ξ	ξ	NOUN
ejpam-1854	7	10	=	=	NOUN
ejpam-1854	7	11	∑∞	∑∞	NOUN
ejpam-1854	7	12	n=1	n=1	PROPN
ejpam-1854	7	13	10−n	10−n	NUM
ejpam-1854	7	14	!	!	PUNCT
ejpam-1854	7	15	can	can	AUX
ejpam-1854	7	16	be	be	AUX
ejpam-1854	7	17	easily	easily	ADV
ejpam-1854	7	18	proved	prove	VERB
ejpam-1854	7	19	from	from	ADP
ejpam-1854	7	20	the	the	DET
ejpam-1854	7	21	liouville	liouville	NOUN
ejpam-1854	7	22	’s	’s	PART
ejpam-1854	7	23	theorem	theorem	NOUN
ejpam-1854	7	24	[	[	X
ejpam-1854	7	25	see	see	VERB
ejpam-1854	7	26	3	3	NUM
ejpam-1854	7	27	]	]	PUNCT
ejpam-1854	7	28	.	.	PUNCT
ejpam-1854	8	1	a	a	DET
ejpam-1854	8	2	real	real	ADJ
ejpam-1854	8	3	number	number	NOUN
ejpam-1854	8	4	ξ	ξ	X
ejpam-1854	8	5	∈	∈	NOUN
ejpam-1854	8	6	r	r	NOUN
ejpam-1854	8	7	is	be	AUX
ejpam-1854	8	8	called	call	VERB
ejpam-1854	8	9	a	a	DET
ejpam-1854	8	10	(	(	PUNCT
ejpam-1854	8	11	real	real	ADJ
ejpam-1854	8	12	)	)	PUNCT
ejpam-1854	8	13	liouville	liouville	NOUN
ejpam-1854	8	14	number	number	NOUN
ejpam-1854	8	15	if	if	SCONJ
ejpam-1854	8	16	for	for	ADP
ejpam-1854	8	17	every	every	DET
ejpam-1854	8	18	positive	positive	ADJ
ejpam-1854	8	19	integer	integer	NOUN
ejpam-1854	8	20	n	n	CCONJ
ejpam-1854	8	21	,	,	PUNCT
ejpam-1854	8	22	there	there	PRON
ejpam-1854	8	23	exist	exist	VERB
ejpam-1854	8	24	integer	integer	NOUN
ejpam-1854	8	25	a	a	PRON
ejpam-1854	8	26	and	and	CCONJ
ejpam-1854	8	27	b	b	NOUN
ejpam-1854	8	28	(	(	PUNCT
ejpam-1854	8	29	>	>	X
ejpam-1854	8	30	1	1	NUM
ejpam-1854	8	31	)	)	PUNCT
ejpam-1854	9	1	such	such	ADJ
ejpam-1854	9	2	that	that	SCONJ
ejpam-1854	9	3	0	0	NUM
ejpam-1854	9	4	<	<	X
ejpam-1854	9	5	�	�	PROPN
ejpam-1854	9	6	�	�	PROPN
ejpam-1854	9	7	�	�	PROPN
ejpam-1854	9	8	ξ−	ξ−	PROPN
ejpam-1854	9	9	a	a	DET
ejpam-1854	9	10	b	b	PROPN
ejpam-1854	9	11	�	�	PROPN
ejpam-1854	9	12	�	�	PROPN
ejpam-1854	9	13	�	�	PROPN
ejpam-1854	9	14	<	<	X
ejpam-1854	9	15	1	1	NUM
ejpam-1854	9	16	bn	bn	NOUN
ejpam-1854	9	17	.	.	PUNCT
ejpam-1854	10	1	real	real	ADJ
ejpam-1854	10	2	liouville	liouville	NOUN
ejpam-1854	10	3	numbers	number	NOUN
ejpam-1854	10	4	have	have	VERB
ejpam-1854	10	5	many	many	ADJ
ejpam-1854	10	6	interesting	interesting	ADJ
ejpam-1854	10	7	properties	property	NOUN
ejpam-1854	10	8	and	and	CCONJ
ejpam-1854	10	9	investigated	investigate	VERB
ejpam-1854	10	10	by	by	ADP
ejpam-1854	10	11	many	many	ADJ
ejpam-1854	10	12	authors	author	NOUN
ejpam-1854	10	13	[	[	X
ejpam-1854	10	14	see	see	VERB
ejpam-1854	10	15	2	2	NUM
ejpam-1854	10	16	,	,	PUNCT
ejpam-1854	10	17	7	7	NUM
ejpam-1854	10	18	,	,	PUNCT
ejpam-1854	10	19	9	9	NUM
ejpam-1854	10	20	,	,	PUNCT
ejpam-1854	10	21	10	10	NUM
ejpam-1854	10	22	,	,	PUNCT
ejpam-1854	10	23	12	12	NUM
ejpam-1854	10	24	,	,	PUNCT
ejpam-1854	10	25	14	14	NUM
ejpam-1854	10	26	]	]	PUNCT
ejpam-1854	10	27	.	.	PUNCT
ejpam-1854	11	1	we	we	PRON
ejpam-1854	11	2	note	note	VERB
ejpam-1854	11	3	that	that	SCONJ
ejpam-1854	11	4	liouville	liouville	NOUN
ejpam-1854	11	5	numbers	number	NOUN
ejpam-1854	11	6	are	be	AUX
ejpam-1854	11	7	real	real	ADJ
ejpam-1854	11	8	numbers	number	NOUN
ejpam-1854	11	9	that	that	PRON
ejpam-1854	11	10	can	can	AUX
ejpam-1854	11	11	be	be	AUX
ejpam-1854	11	12	rapidly	rapidly	ADV
ejpam-1854	11	13	approximated	approximate	VERB
ejpam-1854	11	14	by	by	ADP
ejpam-1854	11	15	algebraic	algebraic	ADJ
ejpam-1854	11	16	numbers	number	NOUN
ejpam-1854	11	17	with	with	ADP
ejpam-1854	11	18	degree	degree	NOUN
ejpam-1854	11	19	one	one	NUM
ejpam-1854	11	20	.	.	PUNCT
ejpam-1854	12	1	a	a	DET
ejpam-1854	12	2	general	general	ADJ
ejpam-1854	12	3	theory	theory	NOUN
ejpam-1854	12	4	of	of	ADP
ejpam-1854	12	5	approximation	approximation	NOUN
ejpam-1854	12	6	by	by	ADP
ejpam-1854	12	7	algebraic	algebraic	ADJ
ejpam-1854	12	8	numbers	number	NOUN
ejpam-1854	12	9	is	be	AUX
ejpam-1854	12	10	given	give	VERB
ejpam-1854	12	11	in	in	ADP
ejpam-1854	12	12	[	[	X
ejpam-1854	12	13	5	5	NUM
ejpam-1854	12	14	]	]	PUNCT
ejpam-1854	12	15	.	.	PUNCT
ejpam-1854	13	1	here	here	ADV
ejpam-1854	13	2	we	we	PRON
ejpam-1854	13	3	mainly	mainly	ADV
ejpam-1854	13	4	focus	focus	VERB
ejpam-1854	13	5	on	on	ADP
ejpam-1854	13	6	the	the	DET
ejpam-1854	13	7	erdös	erdös	PROPN
ejpam-1854	13	8	theorem	theorem	NOUN
ejpam-1854	13	9	:	:	PUNCT
ejpam-1854	13	10	∗corresponding	∗corresponde	VERB
ejpam-1854	13	11	author	author	NOUN
ejpam-1854	13	12	.	.	PUNCT
ejpam-1854	14	1	email	email	NOUN
ejpam-1854	14	2	addresses	address	NOUN
ejpam-1854	14	3	:	:	PUNCT
ejpam-1854	14	4	hmenken@mersin.edu.tr	hmenken@mersin.edu.tr	PROPN
ejpam-1854	14	5	(	(	PUNCT
ejpam-1854	14	6	h.	h.	PROPN
ejpam-1854	14	7	menken	menken	PROPN
ejpam-1854	14	8	)	)	PUNCT
ejpam-1854	14	9	,	,	PUNCT
ejpam-1854	14	10	akadirasan@mersin.edu.tr	akadirasan@mersin.edu.tr	PROPN
ejpam-1854	14	11	(	(	PUNCT
ejpam-1854	14	12	a.	a.	PROPN
ejpam-1854	14	13	aşan	aşan	PROPN
ejpam-1854	14	14	)	)	PUNCT
ejpam-1854	14	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1854	15	1	239	239	NUM
ejpam-1854	15	2	c	c	X
ejpam-1854	15	3	©	©	PROPN
ejpam-1854	15	4	2013	2013	NUM
ejpam-1854	15	5	ejpam	ejpam	NOUN
ejpam-1854	15	6	all	all	DET
ejpam-1854	15	7	rights	right	NOUN
ejpam-1854	15	8	reserved	reserve	VERB
ejpam-1854	15	9	.	.	PUNCT
ejpam-1854	16	1	h.	h.	PROPN
ejpam-1854	16	2	menken	menken	PROPN
ejpam-1854	16	3	,	,	PUNCT
ejpam-1854	16	4	a.	a.	PROPN
ejpam-1854	16	5	aşan	aşan	PROPN
ejpam-1854	16	6	/	/	SYM
ejpam-1854	16	7	eur	eur	PROPN
ejpam-1854	16	8	.	.	PUNCT
ejpam-1854	17	1	j.	j.	PROPN
ejpam-1854	17	2	pure	pure	PROPN
ejpam-1854	17	3	appl	appl	PROPN
ejpam-1854	17	4	.	.	PROPN
ejpam-1854	17	5	math	math	PROPN
ejpam-1854	17	6	,	,	PUNCT
ejpam-1854	17	7	6	6	NUM
ejpam-1854	17	8	(	(	PUNCT
ejpam-1854	17	9	2013	2013	NUM
ejpam-1854	17	10	)	)	PUNCT
ejpam-1854	17	11	,	,	PUNCT
ejpam-1854	17	12	239	239	NUM
ejpam-1854	17	13	-	-	SYM
ejpam-1854	17	14	246	246	NUM
ejpam-1854	17	15	240	240	NUM
ejpam-1854	17	16	theorem	theorem	NOUN
ejpam-1854	17	17	1	1	NUM
ejpam-1854	17	18	.	.	PUNCT
ejpam-1854	18	1	[	[	X
ejpam-1854	18	2	p.	p.	NOUN
ejpam-1854	18	3	erdös	erdös	X
ejpam-1854	18	4	,	,	PUNCT
ejpam-1854	18	5	[	[	X
ejpam-1854	18	6	8	8	NUM
ejpam-1854	18	7	]	]	X
ejpam-1854	18	8	]	]	X
ejpam-1854	18	9	let	let	VERB
ejpam-1854	18	10	a1	a1	NOUN
ejpam-1854	18	11	<	<	X
ejpam-1854	18	12	a2	a2	PROPN
ejpam-1854	18	13	<	<	X
ejpam-1854	18	14	a3	a3	PROPN
ejpam-1854	18	15	<	<	X
ejpam-1854	18	16	.	.	PUNCT
ejpam-1854	18	17	.	.	PUNCT
ejpam-1854	18	18	.	.	PUNCT
ejpam-1854	19	1	be	be	AUX
ejpam-1854	19	2	an	an	DET
ejpam-1854	19	3	infinite	infinite	ADJ
ejpam-1854	19	4	sequence	sequence	NOUN
ejpam-1854	19	5	of	of	ADP
ejpam-1854	19	6	integers	integer	NOUN
ejpam-1854	19	7	satisfying	satisfy	VERB
ejpam-1854	19	8	lim	lim	PROPN
ejpam-1854	19	9	n→∞	n→∞	NUM
ejpam-1854	19	10	sup	sup	NOUN
ejpam-1854	19	11	a	a	DET
ejpam-1854	19	12	1	1	NUM
ejpam-1854	19	13	tn	tn	NOUN
ejpam-1854	19	14	n	n	PRON
ejpam-1854	19	15	=	=	NOUN
ejpam-1854	19	16	∞	∞	NOUN
ejpam-1854	19	17	for	for	ADP
ejpam-1854	19	18	every	every	DET
ejpam-1854	19	19	t	t	PROPN
ejpam-1854	19	20	>	>	X
ejpam-1854	19	21	0	0	NUM
ejpam-1854	19	22	,	,	PUNCT
ejpam-1854	19	23	and	and	CCONJ
ejpam-1854	19	24	an	an	DET
ejpam-1854	19	25	>	>	X
ejpam-1854	19	26	n1+ε	n1+ε	NOUN
ejpam-1854	19	27	for	for	ADP
ejpam-1854	19	28	fixed	fix	VERB
ejpam-1854	19	29	ε	ε	PROPN
ejpam-1854	19	30	>	>	X
ejpam-1854	19	31	0	0	PROPN
ejpam-1854	20	1	and	and	CCONJ
ejpam-1854	20	2	n	n	CCONJ
ejpam-1854	20	3	>	>	X
ejpam-1854	20	4	n0	n0	X
ejpam-1854	20	5	(	(	PUNCT
ejpam-1854	20	6	ε	ε	PROPN
ejpam-1854	20	7	)	)	PUNCT
ejpam-1854	20	8	.	.	PUNCT
ejpam-1854	21	1	then	then	ADV
ejpam-1854	21	2	α=	α=	NOUN
ejpam-1854	21	3	∞	∞	PROPN
ejpam-1854	21	4	∑	∑	PUNCT
ejpam-1854	21	5	n=1	n=1	PROPN
ejpam-1854	21	6	1	1	NUM
ejpam-1854	21	7	an	an	PRON
ejpam-1854	21	8	is	be	AUX
ejpam-1854	21	9	a	a	DET
ejpam-1854	21	10	liouville	liouville	NOUN
ejpam-1854	21	11	number	number	NOUN
ejpam-1854	21	12	.	.	PUNCT
ejpam-1854	22	1	it	it	PRON
ejpam-1854	22	2	is	be	AUX
ejpam-1854	22	3	well	well	ADV
ejpam-1854	22	4	known	know	VERB
ejpam-1854	22	5	that	that	SCONJ
ejpam-1854	22	6	real	real	ADJ
ejpam-1854	22	7	numbers	number	NOUN
ejpam-1854	22	8	field	field	NOUN
ejpam-1854	22	9	r	r	NOUN
ejpam-1854	22	10	is	be	AUX
ejpam-1854	22	11	archimedean	archimedean	ADJ
ejpam-1854	22	12	.	.	PUNCT
ejpam-1854	23	1	there	there	PRON
ejpam-1854	23	2	are	be	VERB
ejpam-1854	23	3	interesting	interesting	ADJ
ejpam-1854	23	4	nonarchimedean	nonarchimedean	ADJ
ejpam-1854	23	5	fields	field	NOUN
ejpam-1854	23	6	as	as	ADP
ejpam-1854	23	7	the	the	DET
ejpam-1854	23	8	p	p	NOUN
ejpam-1854	23	9	-	-	PUNCT
ejpam-1854	23	10	adic	adic	ADJ
ejpam-1854	23	11	numbers	number	NOUN
ejpam-1854	23	12	field	field	VERB
ejpam-1854	23	13	qp	qp	NOUN
ejpam-1854	23	14	and	and	CCONJ
ejpam-1854	23	15	the	the	DET
ejpam-1854	23	16	functions	function	NOUN
ejpam-1854	23	17	field	field	NOUN
ejpam-1854	23	18	.	.	PUNCT
ejpam-1854	24	1	let	let	VERB
ejpam-1854	24	2	p	p	PRON
ejpam-1854	24	3	be	be	AUX
ejpam-1854	24	4	a	a	DET
ejpam-1854	24	5	fixed	fix	VERB
ejpam-1854	24	6	prime	prime	ADJ
ejpam-1854	24	7	number	number	NOUN
ejpam-1854	24	8	.	.	PUNCT
ejpam-1854	25	1	by	by	ADP
ejpam-1854	25	2	zp	zp	PROPN
ejpam-1854	25	3	,	,	PUNCT
ejpam-1854	25	4	qp	qp	PROPN
ejpam-1854	25	5	and	and	CCONJ
ejpam-1854	25	6	cp	cp	INTJ
ejpam-1854	25	7	we	we	PRON
ejpam-1854	25	8	denote	denote	VERB
ejpam-1854	25	9	the	the	DET
ejpam-1854	25	10	ring	ring	NOUN
ejpam-1854	25	11	of	of	ADP
ejpam-1854	25	12	p	p	NOUN
ejpam-1854	25	13	-	-	PUNCT
ejpam-1854	25	14	adic	adic	ADJ
ejpam-1854	25	15	integers	integer	NOUN
ejpam-1854	25	16	,	,	PUNCT
ejpam-1854	25	17	the	the	DET
ejpam-1854	25	18	field	field	NOUN
ejpam-1854	25	19	of	of	ADP
ejpam-1854	25	20	p	p	NOUN
ejpam-1854	25	21	-	-	PUNCT
ejpam-1854	25	22	adic	adic	ADJ
ejpam-1854	25	23	numbers	number	NOUN
ejpam-1854	25	24	,	,	PUNCT
ejpam-1854	25	25	and	and	CCONJ
ejpam-1854	25	26	the	the	DET
ejpam-1854	25	27	completion	completion	NOUN
ejpam-1854	25	28	of	of	ADP
ejpam-1854	25	29	the	the	DET
ejpam-1854	25	30	algebraic	algebraic	ADJ
ejpam-1854	25	31	closure	closure	NOUN
ejpam-1854	25	32	of	of	ADP
ejpam-1854	25	33	qp	qp	NOUN
ejpam-1854	25	34	,	,	PUNCT
ejpam-1854	25	35	respectively	respectively	ADV
ejpam-1854	25	36	.	.	PUNCT
ejpam-1854	26	1	in	in	ADP
ejpam-1854	26	2	the	the	DET
ejpam-1854	26	3	present	present	ADJ
ejpam-1854	26	4	work	work	NOUN
ejpam-1854	26	5	we	we	PRON
ejpam-1854	26	6	investigate	investigate	VERB
ejpam-1854	26	7	some	some	DET
ejpam-1854	26	8	properties	property	NOUN
ejpam-1854	26	9	of	of	ADP
ejpam-1854	26	10	liouville	liouville	NOUN
ejpam-1854	26	11	numbers	number	NOUN
ejpam-1854	26	12	in	in	ADP
ejpam-1854	26	13	non	non	ADJ
ejpam-1854	26	14	-	-	ADJ
ejpam-1854	26	15	archimedean	archimedean	ADJ
ejpam-1854	26	16	case	case	NOUN
ejpam-1854	26	17	.	.	PUNCT
ejpam-1854	27	1	mainly	mainly	ADV
ejpam-1854	27	2	,	,	PUNCT
ejpam-1854	27	3	we	we	PRON
ejpam-1854	27	4	give	give	VERB
ejpam-1854	27	5	the	the	DET
ejpam-1854	27	6	analogues	analogue	NOUN
ejpam-1854	27	7	of	of	ADP
ejpam-1854	27	8	the	the	DET
ejpam-1854	27	9	erdös	erdös	PROPN
ejpam-1854	27	10	theorem	theorem	NOUN
ejpam-1854	27	11	in	in	ADP
ejpam-1854	27	12	the	the	DET
ejpam-1854	27	13	non	non	ADJ
ejpam-1854	27	14	-	-	ADJ
ejpam-1854	27	15	archimedean	archimedean	ADJ
ejpam-1854	27	16	case	case	NOUN
ejpam-1854	27	17	,	,	PUNCT
ejpam-1854	27	18	both	both	PRON
ejpam-1854	27	19	in	in	ADP
ejpam-1854	27	20	p	p	ADJ
ejpam-1854	27	21	-	-	PUNCT
ejpam-1854	27	22	adic	adic	ADJ
ejpam-1854	27	23	numbers	number	NOUN
ejpam-1854	27	24	field	field	VERB
ejpam-1854	27	25	qp	qp	NOUN
ejpam-1854	27	26	and	and	CCONJ
ejpam-1854	27	27	the	the	DET
ejpam-1854	27	28	functions	function	NOUN
ejpam-1854	27	29	field	field	NOUN
ejpam-1854	27	30	k	k	PROPN
ejpam-1854	27	31	〈	〈	PROPN
ejpam-1854	27	32	x	x	X
ejpam-1854	27	33	〉	〉	NOUN
ejpam-1854	27	34	.	.	PUNCT
ejpam-1854	28	1	although	although	SCONJ
ejpam-1854	28	2	the	the	DET
ejpam-1854	28	3	classical	classical	ADJ
ejpam-1854	28	4	liouville	liouville	NOUN
ejpam-1854	28	5	numbers	number	NOUN
ejpam-1854	28	6	are	be	AUX
ejpam-1854	28	7	real	real	ADJ
ejpam-1854	28	8	numbers	number	NOUN
ejpam-1854	28	9	that	that	PRON
ejpam-1854	28	10	can	can	AUX
ejpam-1854	28	11	be	be	AUX
ejpam-1854	28	12	rapidly	rapidly	ADV
ejpam-1854	28	13	approximated	approximate	VERB
ejpam-1854	28	14	by	by	ADP
ejpam-1854	28	15	rational	rational	ADJ
ejpam-1854	28	16	numbers	number	NOUN
ejpam-1854	28	17	,	,	PUNCT
ejpam-1854	28	18	the	the	DET
ejpam-1854	28	19	p	p	NOUN
ejpam-1854	28	20	-	-	PUNCT
ejpam-1854	28	21	adic	adic	ADJ
ejpam-1854	28	22	liouville	liouville	NOUN
ejpam-1854	28	23	numbers	number	NOUN
ejpam-1854	28	24	are	be	AUX
ejpam-1854	28	25	those	those	DET
ejpam-1854	28	26	numbers	number	NOUN
ejpam-1854	28	27	that	that	PRON
ejpam-1854	28	28	can	can	AUX
ejpam-1854	28	29	be	be	AUX
ejpam-1854	28	30	rapidly	rapidly	ADV
ejpam-1854	28	31	approximated	approximate	VERB
ejpam-1854	28	32	by	by	ADP
ejpam-1854	28	33	positive	positive	ADJ
ejpam-1854	28	34	integers	integer	NOUN
ejpam-1854	28	35	in	in	ADP
ejpam-1854	28	36	the	the	DET
ejpam-1854	28	37	p	p	NOUN
ejpam-1854	28	38	-	-	PUNCT
ejpam-1854	28	39	adic	adic	ADJ
ejpam-1854	28	40	norm	norm	NOUN
ejpam-1854	28	41	.	.	PUNCT
ejpam-1854	29	1	the	the	DET
ejpam-1854	29	2	p	p	NOUN
ejpam-1854	29	3	-	-	PUNCT
ejpam-1854	29	4	adic	adic	ADJ
ejpam-1854	29	5	liouville	liouville	NOUN
ejpam-1854	29	6	numbers	number	NOUN
ejpam-1854	29	7	are	be	AUX
ejpam-1854	29	8	defined	define	VERB
ejpam-1854	29	9	as	as	SCONJ
ejpam-1854	29	10	follows	follow	VERB
ejpam-1854	29	11	:	:	PUNCT
ejpam-1854	29	12	definition	definition	NOUN
ejpam-1854	29	13	1	1	NUM
ejpam-1854	29	14	(	(	PUNCT
ejpam-1854	29	15	[	[	X
ejpam-1854	29	16	6	6	NUM
ejpam-1854	29	17	,	,	PUNCT
ejpam-1854	29	18	21	21	NUM
ejpam-1854	29	19	]	]	PUNCT
ejpam-1854	29	20	)	)	PUNCT
ejpam-1854	29	21	.	.	PUNCT
ejpam-1854	30	1	let	let	VERB
ejpam-1854	30	2	α	α	PRON
ejpam-1854	30	3	be	be	AUX
ejpam-1854	30	4	a	a	DET
ejpam-1854	30	5	p	p	ADJ
ejpam-1854	30	6	-	-	PUNCT
ejpam-1854	30	7	adic	adic	ADJ
ejpam-1854	30	8	integer	integer	NOUN
ejpam-1854	30	9	.	.	PUNCT
ejpam-1854	31	1	if	if	SCONJ
ejpam-1854	31	2	lim	lim	PROPN
ejpam-1854	31	3	n→∞	n→∞	PRON
ejpam-1854	31	4	inf	inf	PROPN
ejpam-1854	31	5	n	n	PROPN
ejpam-1854	31	6	p	p	NOUN
ejpam-1854	31	7	|n−α|p	|n−α|p	PROPN
ejpam-1854	31	8	=	=	SYM
ejpam-1854	31	9	0	0	NUM
ejpam-1854	31	10	,	,	PUNCT
ejpam-1854	31	11	then	then	ADV
ejpam-1854	31	12	the	the	DET
ejpam-1854	31	13	number	number	NOUN
ejpam-1854	31	14	α	α	NOUN
ejpam-1854	31	15	is	be	AUX
ejpam-1854	31	16	called	call	VERB
ejpam-1854	31	17	p	p	ADJ
ejpam-1854	31	18	-	-	PUNCT
ejpam-1854	31	19	adic	adic	ADJ
ejpam-1854	31	20	liouville	liouville	NOUN
ejpam-1854	31	21	number	number	NOUN
ejpam-1854	31	22	.	.	PUNCT
ejpam-1854	31	23	example	example	NOUN
ejpam-1854	32	1	1	1	NUM
ejpam-1854	32	2	.	.	PUNCT
ejpam-1854	32	3	let	let	AUX
ejpam-1854	32	4	consider	consider	VERB
ejpam-1854	32	5	the	the	DET
ejpam-1854	32	6	series	series	NOUN
ejpam-1854	32	7	α	α	NOUN
ejpam-1854	32	8	=	=	SYM
ejpam-1854	32	9	∑∞	∑∞	NOUN
ejpam-1854	32	10	n=0	n=0	X
ejpam-1854	32	11	pn	pn	NOUN
ejpam-1854	32	12	!	!	PUNCT
ejpam-1854	32	13	.	.	PUNCT
ejpam-1854	33	1	it	it	PRON
ejpam-1854	33	2	is	be	AUX
ejpam-1854	33	3	easy	easy	ADJ
ejpam-1854	33	4	to	to	PART
ejpam-1854	33	5	see	see	VERB
ejpam-1854	33	6	that	that	SCONJ
ejpam-1854	33	7	the	the	DET
ejpam-1854	33	8	sum	sum	NOUN
ejpam-1854	33	9	is	be	AUX
ejpam-1854	33	10	a	a	DET
ejpam-1854	33	11	p	p	ADJ
ejpam-1854	33	12	-	-	PUNCT
ejpam-1854	33	13	adic	adic	ADJ
ejpam-1854	33	14	liouville	liouville	NOUN
ejpam-1854	33	15	number	number	NOUN
ejpam-1854	33	16	.	.	PUNCT
ejpam-1854	34	1	the	the	DET
ejpam-1854	34	2	definition	definition	NOUN
ejpam-1854	34	3	above	above	ADV
ejpam-1854	34	4	is	be	AUX
ejpam-1854	34	5	first	first	ADV
ejpam-1854	34	6	introduced	introduce	VERB
ejpam-1854	34	7	by	by	ADP
ejpam-1854	34	8	d.	d.	PROPN
ejpam-1854	34	9	clark	clark	PROPN
ejpam-1854	35	1	[	[	X
ejpam-1854	35	2	6	6	NUM
ejpam-1854	35	3	]	]	PUNCT
ejpam-1854	35	4	and	and	CCONJ
ejpam-1854	35	5	it	it	PRON
ejpam-1854	35	6	is	be	AUX
ejpam-1854	35	7	better	well	ADV
ejpam-1854	35	8	adapted	adapt	VERB
ejpam-1854	35	9	to	to	ADP
ejpam-1854	35	10	differential	differential	ADJ
ejpam-1854	35	11	equations	equation	NOUN
ejpam-1854	35	12	.	.	PUNCT
ejpam-1854	36	1	in	in	ADP
ejpam-1854	36	2	fact	fact	NOUN
ejpam-1854	36	3	,	,	PUNCT
ejpam-1854	36	4	consider	consider	VERB
ejpam-1854	36	5	the	the	DET
ejpam-1854	36	6	differential	differential	ADJ
ejpam-1854	36	7	equation	equation	NOUN
ejpam-1854	36	8	x	x	X
ejpam-1854	37	1	f	f	X
ejpam-1854	37	2	′(x)−λ	′(x)−λ	PROPN
ejpam-1854	37	3	f	f	PROPN
ejpam-1854	37	4	(	(	PUNCT
ejpam-1854	37	5	x	x	X
ejpam-1854	37	6	)	)	PUNCT
ejpam-1854	37	7	=	=	SYM
ejpam-1854	37	8	1	1	NUM
ejpam-1854	37	9	1−	1−	NUM
ejpam-1854	37	10	x	x	PUNCT
ejpam-1854	37	11	on	on	ADP
ejpam-1854	37	12	a	a	DET
ejpam-1854	37	13	neighborhood	neighborhood	NOUN
ejpam-1854	37	14	d	d	NOUN
ejpam-1854	37	15	of	of	ADP
ejpam-1854	37	16	0	0	NUM
ejpam-1854	37	17	in	in	ADP
ejpam-1854	37	18	zp	zp	PROPN
ejpam-1854	37	19	where	where	SCONJ
ejpam-1854	37	20	λ	λ	PROPN
ejpam-1854	37	21	∈	∈	PROPN
ejpam-1854	37	22	zp\{0,1	zp\{0,1	PROPN
ejpam-1854	37	23	,	,	PUNCT
ejpam-1854	37	24	2	2	NUM
ejpam-1854	37	25	,	,	PUNCT
ejpam-1854	37	26	.	.	PUNCT
ejpam-1854	37	27	.	.	PUNCT
ejpam-1854	37	28	.	.	PUNCT
ejpam-1854	37	29	}	}	PUNCT
ejpam-1854	37	30	.	.	PUNCT
ejpam-1854	38	1	this	this	DET
ejpam-1854	38	2	equation	equation	NOUN
ejpam-1854	38	3	has	have	VERB
ejpam-1854	38	4	an	an	DET
ejpam-1854	38	5	unique	unique	ADJ
ejpam-1854	38	6	formal	formal	ADJ
ejpam-1854	38	7	solution	solution	NOUN
ejpam-1854	38	8	,	,	PUNCT
ejpam-1854	38	9	namely	namely	ADV
ejpam-1854	38	10	,	,	PUNCT
ejpam-1854	38	11	f	f	PROPN
ejpam-1854	38	12	(	(	PUNCT
ejpam-1854	38	13	x	x	NOUN
ejpam-1854	38	14	)	)	PUNCT
ejpam-1854	38	15	=	=	NOUN
ejpam-1854	38	16	∑∞	∑∞	NOUN
ejpam-1854	38	17	n=1	n=1	PROPN
ejpam-1854	38	18	1	1	NUM
ejpam-1854	38	19	n−λ	n−λ	NOUN
ejpam-1854	38	20	xn	xn	INTJ
ejpam-1854	38	21	.	.	PUNCT
ejpam-1854	39	1	it	it	PRON
ejpam-1854	39	2	is	be	AUX
ejpam-1854	39	3	clear	clear	ADJ
ejpam-1854	39	4	that	that	SCONJ
ejpam-1854	39	5	this	this	DET
ejpam-1854	39	6	solution	solution	NOUN
ejpam-1854	39	7	divergent	divergent	ADJ
ejpam-1854	39	8	if	if	SCONJ
ejpam-1854	39	9	only	only	ADV
ejpam-1854	39	10	if	if	SCONJ
ejpam-1854	39	11	λ	λ	NOUN
ejpam-1854	39	12	is	be	AUX
ejpam-1854	39	13	a	a	DET
ejpam-1854	39	14	p	p	ADJ
ejpam-1854	39	15	-	-	PUNCT
ejpam-1854	39	16	adic	adic	ADJ
ejpam-1854	39	17	liouville	liouville	NOUN
ejpam-1854	39	18	number	number	NOUN
ejpam-1854	39	19	(	(	PUNCT
ejpam-1854	39	20	for	for	ADP
ejpam-1854	39	21	details	detail	NOUN
ejpam-1854	39	22	see	see	VERB
ejpam-1854	39	23	[	[	X
ejpam-1854	39	24	20	20	NUM
ejpam-1854	39	25	]	]	NUM
ejpam-1854	39	26	)	)	PUNCT
ejpam-1854	39	27	.	.	PUNCT
ejpam-1854	40	1	it	it	PRON
ejpam-1854	40	2	is	be	AUX
ejpam-1854	40	3	well	well	ADV
ejpam-1854	40	4	known	know	VERB
ejpam-1854	40	5	that	that	SCONJ
ejpam-1854	40	6	the	the	DET
ejpam-1854	40	7	set	set	ADJ
ejpam-1854	40	8	l	l	NOUN
ejpam-1854	40	9	of	of	ADP
ejpam-1854	40	10	p	p	NOUN
ejpam-1854	40	11	-	-	PUNCT
ejpam-1854	40	12	adic	adic	ADJ
ejpam-1854	40	13	liouville	liouville	NOUN
ejpam-1854	40	14	numbers	number	NOUN
ejpam-1854	40	15	have	have	VERB
ejpam-1854	40	16	the	the	DET
ejpam-1854	40	17	following	following	ADJ
ejpam-1854	40	18	basic	basic	ADJ
ejpam-1854	40	19	properties	property	NOUN
ejpam-1854	40	20	:	:	PUNCT
ejpam-1854	41	1	1	1	X
ejpam-1854	41	2	.	.	X
ejpam-1854	41	3	l	l	NOUN
ejpam-1854	41	4	⊂	⊂	PROPN
ejpam-1854	42	1	zp	zp	PROPN
ejpam-1854	42	2	h.	h.	PROPN
ejpam-1854	42	3	menken	menken	PROPN
ejpam-1854	42	4	,	,	PUNCT
ejpam-1854	42	5	a.	a.	PROPN
ejpam-1854	42	6	aşan	aşan	PROPN
ejpam-1854	42	7	/	/	SYM
ejpam-1854	42	8	eur	eur	PROPN
ejpam-1854	42	9	.	.	PUNCT
ejpam-1854	43	1	j.	j.	PROPN
ejpam-1854	43	2	pure	pure	PROPN
ejpam-1854	43	3	appl	appl	PROPN
ejpam-1854	43	4	.	.	PROPN
ejpam-1854	43	5	math	math	PROPN
ejpam-1854	43	6	,	,	PUNCT
ejpam-1854	43	7	6	6	NUM
ejpam-1854	43	8	(	(	PUNCT
ejpam-1854	43	9	2013	2013	NUM
ejpam-1854	43	10	)	)	PUNCT
ejpam-1854	43	11	,	,	PUNCT
ejpam-1854	43	12	239	239	NUM
ejpam-1854	43	13	-	-	SYM
ejpam-1854	43	14	246	246	NUM
ejpam-1854	43	15	241	241	NUM
ejpam-1854	43	16	2	2	NUM
ejpam-1854	43	17	.	.	PUNCT
ejpam-1854	44	1	l	l	NOUN
ejpam-1854	44	2	has	have	VERB
ejpam-1854	44	3	measure	measure	NOUN
ejpam-1854	44	4	0	0	NUM
ejpam-1854	44	5	for	for	ADP
ejpam-1854	44	6	the	the	DET
ejpam-1854	44	7	real	real	ADJ
ejpam-1854	44	8	haar	haar	NOUN
ejpam-1854	44	9	measure	measure	NOUN
ejpam-1854	44	10	on	on	ADP
ejpam-1854	44	11	zp	zp	PROPN
ejpam-1854	44	12	3	3	NUM
ejpam-1854	44	13	.	.	PUNCT
ejpam-1854	45	1	if	if	SCONJ
ejpam-1854	45	2	α	α	PRON
ejpam-1854	45	3	∈	∈	PROPN
ejpam-1854	45	4	l	l	NOUN
ejpam-1854	45	5	and	and	CCONJ
ejpam-1854	45	6	n	n	CCONJ
ejpam-1854	45	7	,	,	PUNCT
ejpam-1854	45	8	m	m	VERB
ejpam-1854	45	9	∈	∈	PROPN
ejpam-1854	45	10	z	z	NOUN
ejpam-1854	45	11	with	with	ADP
ejpam-1854	45	12	m	m	PROPN
ejpam-1854	45	13	>	>	X
ejpam-1854	45	14	0	0	PROPN
ejpam-1854	45	15	,	,	PUNCT
ejpam-1854	45	16	the	the	DET
ejpam-1854	45	17	n+mα	n+mα	NOUN
ejpam-1854	45	18	∈	∈	PROPN
ejpam-1854	45	19	l	l	NOUN
ejpam-1854	45	20	4	4	X
ejpam-1854	45	21	.	.	PUNCT
ejpam-1854	46	1	l	l	NOUN
ejpam-1854	46	2	6=−l	6=−l	NUM
ejpam-1854	46	3	and	and	CCONJ
ejpam-1854	46	4	l	l	NOUN
ejpam-1854	46	5	∩−l	∩−l	NOUN
ejpam-1854	46	6	6=	6=	NUM
ejpam-1854	46	7	;	;	PUNCT
ejpam-1854	46	8	5	5	X
ejpam-1854	46	9	.	.	X
ejpam-1854	46	10	l	l	NOUN
ejpam-1854	46	11	forms	form	VERB
ejpam-1854	46	12	a	a	DET
ejpam-1854	46	13	dense	dense	ADJ
ejpam-1854	46	14	subset	subset	NOUN
ejpam-1854	46	15	of	of	ADP
ejpam-1854	46	16	zp	zp	PROPN
ejpam-1854	46	17	6	6	NUM
ejpam-1854	46	18	.	.	PUNCT
ejpam-1854	47	1	every	every	DET
ejpam-1854	47	2	α	α	PROPN
ejpam-1854	47	3	∈	∈	PROPN
ejpam-1854	47	4	l	l	NOUN
ejpam-1854	47	5	is	be	AUX
ejpam-1854	47	6	transcendental	transcendental	ADJ
ejpam-1854	47	7	over	over	ADP
ejpam-1854	47	8	q.	q.	PROPN
ejpam-1854	47	9	in	in	ADP
ejpam-1854	47	10	general	general	ADJ
ejpam-1854	47	11	case	case	NOUN
ejpam-1854	47	12	the	the	DET
ejpam-1854	47	13	p	p	NOUN
ejpam-1854	47	14	-	-	PUNCT
ejpam-1854	47	15	adic	adic	ADJ
ejpam-1854	47	16	transcendental	transcendental	ADJ
ejpam-1854	47	17	numbers	number	NOUN
ejpam-1854	47	18	have	have	AUX
ejpam-1854	47	19	been	be	AUX
ejpam-1854	47	20	studied	study	VERB
ejpam-1854	47	21	by	by	ADP
ejpam-1854	47	22	k.	k.	PROPN
ejpam-1854	47	23	mahler	mahler	PROPN
ejpam-1854	48	1	[	[	X
ejpam-1854	48	2	15	15	NUM
ejpam-1854	48	3	]	]	X
ejpam-1854	48	4	,	,	PUNCT
ejpam-1854	48	5	w.	w.	PROPN
ejpam-1854	48	6	w.	w.	PROPN
ejpam-1854	48	7	adams	adams	PROPN
ejpam-1854	49	1	[	[	X
ejpam-1854	49	2	1	1	NUM
ejpam-1854	49	3	]	]	PUNCT
ejpam-1854	49	4	,	,	PUNCT
ejpam-1854	49	5	x.	x.	PROPN
ejpam-1854	49	6	x.	x.	PROPN
ejpam-1854	50	1	long	long	PROPN
ejpam-1854	51	1	[	[	X
ejpam-1854	51	2	13	13	NUM
ejpam-1854	51	3	]	]	PUNCT
ejpam-1854	51	4	,	,	PUNCT
ejpam-1854	51	5	k.	k.	PROPN
ejpam-1854	51	6	nishioka	nishioka	VERB
ejpam-1854	52	1	[	[	X
ejpam-1854	52	2	19	19	NUM
ejpam-1854	52	3	]	]	PUNCT
ejpam-1854	52	4	and	and	CCONJ
ejpam-1854	52	5	others	other	NOUN
ejpam-1854	52	6	.	.	PUNCT
ejpam-1854	53	1	as	as	ADP
ejpam-1854	53	2	a	a	DET
ejpam-1854	53	3	special	special	ADJ
ejpam-1854	53	4	case	case	NOUN
ejpam-1854	53	5	the	the	DET
ejpam-1854	53	6	p	p	NOUN
ejpam-1854	53	7	-	-	PUNCT
ejpam-1854	53	8	adic	adic	ADJ
ejpam-1854	53	9	liouville	liouville	NOUN
ejpam-1854	53	10	numbers	number	NOUN
ejpam-1854	53	11	have	have	AUX
ejpam-1854	53	12	been	be	AUX
ejpam-1854	53	13	studied	study	VERB
ejpam-1854	53	14	in	in	ADP
ejpam-1854	53	15	[	[	X
ejpam-1854	53	16	4	4	NUM
ejpam-1854	53	17	,	,	PUNCT
ejpam-1854	53	18	11	11	NUM
ejpam-1854	53	19	,	,	PUNCT
ejpam-1854	53	20	17	17	NUM
ejpam-1854	53	21	,	,	PUNCT
ejpam-1854	53	22	18	18	NUM
ejpam-1854	53	23	]	]	PUNCT
ejpam-1854	53	24	and	and	CCONJ
ejpam-1854	53	25	others	other	NOUN
ejpam-1854	53	26	.	.	PUNCT
ejpam-1854	54	1	2	2	X
ejpam-1854	54	2	.	.	X
ejpam-1854	54	3	the	the	DET
ejpam-1854	54	4	erdös	erdös	PROPN
ejpam-1854	54	5	theorem	theorem	NOUN
ejpam-1854	54	6	in	in	ADP
ejpam-1854	54	7	the	the	DET
ejpam-1854	54	8	p	p	NOUN
ejpam-1854	54	9	-	-	PUNCT
ejpam-1854	54	10	adic	adic	ADJ
ejpam-1854	54	11	numbers	number	NOUN
ejpam-1854	54	12	field	field	VERB
ejpam-1854	54	13	qp	qp	NOUN
ejpam-1854	54	14	.	.	PUNCT
ejpam-1854	55	1	we	we	PRON
ejpam-1854	55	2	prove	prove	VERB
ejpam-1854	55	3	the	the	DET
ejpam-1854	55	4	following	follow	VERB
ejpam-1854	55	5	result	result	NOUN
ejpam-1854	55	6	as	as	ADP
ejpam-1854	55	7	an	an	DET
ejpam-1854	55	8	analogue	analogue	NOUN
ejpam-1854	55	9	of	of	ADP
ejpam-1854	55	10	the	the	DET
ejpam-1854	55	11	erdös	erdös	PROPN
ejpam-1854	55	12	theorem	theorem	NOUN
ejpam-1854	55	13	in	in	ADP
ejpam-1854	55	14	the	the	DET
ejpam-1854	55	15	p	p	NOUN
ejpam-1854	55	16	-	-	PUNCT
ejpam-1854	55	17	adic	adic	ADJ
ejpam-1854	55	18	numbers	number	NOUN
ejpam-1854	55	19	field	field	PROPN
ejpam-1854	55	20	qp	qp	PROPN
ejpam-1854	55	21	.	.	PUNCT
ejpam-1854	55	22	theorem	theorem	PROPN
ejpam-1854	55	23	2	2	NUM
ejpam-1854	55	24	.	.	PUNCT
ejpam-1854	56	1	let	let	VERB
ejpam-1854	56	2	�	�	PROPN
ejpam-1854	56	3	an	an	DET
ejpam-1854	56	4	�	�	PROPN
ejpam-1854	56	5	be	be	AUX
ejpam-1854	56	6	a	a	DET
ejpam-1854	56	7	sequence	sequence	NOUN
ejpam-1854	56	8	of	of	ADP
ejpam-1854	56	9	p	p	NOUN
ejpam-1854	56	10	-	-	PUNCT
ejpam-1854	56	11	adic	adic	ADJ
ejpam-1854	56	12	integers	integer	NOUN
ejpam-1854	56	13	such	such	ADJ
ejpam-1854	56	14	that	that	SCONJ
ejpam-1854	56	15	νp	νp	ADP
ejpam-1854	56	16	�	�	PROPN
ejpam-1854	56	17	an	an	DET
ejpam-1854	56	18	�	�	PROPN
ejpam-1854	56	19	<	<	X
ejpam-1854	56	20	νp	νp	PRON
ejpam-1854	56	21	�	�	PROPN
ejpam-1854	56	22	an+1	an+1	PROPN
ejpam-1854	56	23	�	�	PROPN
ejpam-1854	56	24	(	(	PUNCT
ejpam-1854	56	25	1	1	NUM
ejpam-1854	56	26	)	)	PUNCT
ejpam-1854	56	27	for	for	ADP
ejpam-1854	56	28	every	every	DET
ejpam-1854	56	29	n	n	CCONJ
ejpam-1854	56	30	,	,	PUNCT
ejpam-1854	56	31	and	and	CCONJ
ejpam-1854	57	1	νp	νp	PRON
ejpam-1854	57	2	�	�	PROPN
ejpam-1854	57	3	an+1	an+1	PROPN
ejpam-1854	57	4	�	�	PROPN
ejpam-1854	57	5	≥	≥	PRON
ejpam-1854	57	6	n1+ε	n1+ε	PROPN
ejpam-1854	57	7	(	(	PUNCT
ejpam-1854	57	8	2	2	NUM
ejpam-1854	57	9	)	)	PUNCT
ejpam-1854	57	10	for	for	ADP
ejpam-1854	57	11	fixed	fix	VERB
ejpam-1854	57	12	ε	ε	PROPN
ejpam-1854	57	13	>	>	X
ejpam-1854	57	14	0	0	PROPN
ejpam-1854	57	15	and	and	CCONJ
ejpam-1854	57	16	n	n	CCONJ
ejpam-1854	57	17	>	>	X
ejpam-1854	57	18	n0	n0	X
ejpam-1854	57	19	(	(	PUNCT
ejpam-1854	57	20	ε	ε	PROPN
ejpam-1854	57	21	)	)	PUNCT
ejpam-1854	57	22	.	.	PUNCT
ejpam-1854	58	1	then	then	ADV
ejpam-1854	58	2	α=	α=	NOUN
ejpam-1854	58	3	∞	∞	PROPN
ejpam-1854	58	4	∑	∑	PROPN
ejpam-1854	58	5	n=1	n=1	PROPN
ejpam-1854	58	6	an	an	PRON
ejpam-1854	58	7	is	be	AUX
ejpam-1854	58	8	a	a	DET
ejpam-1854	58	9	p	p	ADJ
ejpam-1854	58	10	-	-	PUNCT
ejpam-1854	58	11	adic	adic	ADJ
ejpam-1854	58	12	liouville	liouville	NOUN
ejpam-1854	58	13	number	number	NOUN
ejpam-1854	58	14	.	.	PUNCT
ejpam-1854	59	1	proof	proof	NOUN
ejpam-1854	59	2	.	.	PUNCT
ejpam-1854	60	1	first	first	ADV
ejpam-1854	60	2	we	we	PRON
ejpam-1854	60	3	show	show	VERB
ejpam-1854	60	4	that	that	SCONJ
ejpam-1854	60	5	the	the	DET
ejpam-1854	60	6	series	series	PROPN
ejpam-1854	60	7	∑∞	∑∞	PROPN
ejpam-1854	60	8	n=1	n=1	PROPN
ejpam-1854	60	9	an	an	PRON
ejpam-1854	60	10	is	be	AUX
ejpam-1854	60	11	convergent	convergent	ADJ
ejpam-1854	60	12	.	.	PUNCT
ejpam-1854	61	1	it	it	PRON
ejpam-1854	61	2	follows	follow	VERB
ejpam-1854	61	3	from	from	ADP
ejpam-1854	61	4	the	the	DET
ejpam-1854	61	5	condition	condition	NOUN
ejpam-1854	61	6	(	(	PUNCT
ejpam-1854	61	7	2	2	NUM
ejpam-1854	61	8	)	)	PUNCT
ejpam-1854	61	9	that	that	PRON
ejpam-1854	61	10	νp	νp	ADP
ejpam-1854	61	11	�	�	PROPN
ejpam-1854	61	12	an+1	an+1	PROPN
ejpam-1854	61	13	�	�	PROPN
ejpam-1854	61	14	≥	≥	PUNCT
ejpam-1854	61	15	n1+ε	n1+ε	PROPN
ejpam-1854	61	16	for	for	ADP
ejpam-1854	61	17	fixed	fix	VERB
ejpam-1854	61	18	ε	ε	PROPN
ejpam-1854	61	19	>	>	X
ejpam-1854	61	20	0	0	PROPN
ejpam-1854	61	21	and	and	CCONJ
ejpam-1854	61	22	n	n	CCONJ
ejpam-1854	61	23	>	>	X
ejpam-1854	61	24	n0	n0	X
ejpam-1854	61	25	(	(	PUNCT
ejpam-1854	61	26	ε	ε	PROPN
ejpam-1854	61	27	)	)	PUNCT
ejpam-1854	61	28	.	.	PUNCT
ejpam-1854	62	1	then	then	ADV
ejpam-1854	62	2	,	,	PUNCT
ejpam-1854	62	3	we	we	PRON
ejpam-1854	62	4	have	have	VERB
ejpam-1854	62	5	�	�	PROPN
ejpam-1854	62	6	�	�	PROPN
ejpam-1854	62	7	an+1	an+1	NOUN
ejpam-1854	62	8	�	�	PROPN
ejpam-1854	62	9	�	�	PROPN
ejpam-1854	62	10	p	p	NOUN
ejpam-1854	62	11	=	=	NOUN
ejpam-1854	62	12	p−νp(an+1	p−νp(an+1	PROPN
ejpam-1854	62	13	)	)	PUNCT
ejpam-1854	62	14	≤	≤	NOUN
ejpam-1854	62	15	p−n1+ε	p−n1+ε	NOUN
ejpam-1854	62	16	→	→	SYM
ejpam-1854	62	17	0	0	NUM
ejpam-1854	62	18	,	,	PUNCT
ejpam-1854	62	19	(	(	PUNCT
ejpam-1854	62	20	n→∞	n→∞	NUM
ejpam-1854	62	21	)	)	PUNCT
ejpam-1854	62	22	.	.	PUNCT
ejpam-1854	63	1	hence	hence	ADV
ejpam-1854	63	2	,	,	PUNCT
ejpam-1854	63	3	lim	lim	PROPN
ejpam-1854	63	4	n→0	n→0	PROPN
ejpam-1854	64	1	an	an	PROPN
ejpam-1854	64	2	=	=	SYM
ejpam-1854	64	3	0	0	NUM
ejpam-1854	64	4	,	,	PUNCT
ejpam-1854	64	5	so	so	ADV
ejpam-1854	64	6	the	the	DET
ejpam-1854	64	7	series	series	NOUN
ejpam-1854	64	8	∑∞	∑∞	PROPN
ejpam-1854	64	9	n=1	n=1	PROPN
ejpam-1854	64	10	an	an	PRON
ejpam-1854	64	11	is	be	AUX
ejpam-1854	64	12	convergent	convergent	NOUN
ejpam-1854	64	13	.	.	PUNCT
ejpam-1854	65	1	by	by	ADP
ejpam-1854	65	2	the	the	DET
ejpam-1854	65	3	property	property	NOUN
ejpam-1854	65	4	�	�	PROPN
ejpam-1854	65	5	�	�	PROPN
ejpam-1854	65	6	∑∞	∑∞	PROPN
ejpam-1854	65	7	n=1	n=1	PROPN
ejpam-1854	65	8	an	an	DET
ejpam-1854	65	9	�	�	PROPN
ejpam-1854	65	10	�	�	PROPN
ejpam-1854	65	11	p	p	PROPN
ejpam-1854	65	12	≤max	≤max	PROPN
ejpam-1854	65	13	n∈n	n∈n	NUM
ejpam-1854	65	14	�	�	PROPN
ejpam-1854	65	15	�	�	PROPN
ejpam-1854	65	16	an	an	DET
ejpam-1854	65	17	�	�	PROPN
ejpam-1854	65	18	�	�	PROPN
ejpam-1854	65	19	p	p	NOUN
ejpam-1854	65	20	,	,	PUNCT
ejpam-1854	65	21	we	we	PRON
ejpam-1854	65	22	obtain	obtain	VERB
ejpam-1854	65	23	that	that	SCONJ
ejpam-1854	65	24	α=	α=	NOUN
ejpam-1854	65	25	∑∞	∑∞	NOUN
ejpam-1854	65	26	n=1	n=1	PUNCT
ejpam-1854	65	27	an	an	DET
ejpam-1854	65	28	∈	∈	PROPN
ejpam-1854	65	29	zp	zp	PROPN
ejpam-1854	65	30	.	.	PUNCT
ejpam-1854	66	1	also	also	ADV
ejpam-1854	66	2	,	,	PUNCT
ejpam-1854	66	3	by	by	ADP
ejpam-1854	66	4	the	the	DET
ejpam-1854	66	5	condition	condition	NOUN
ejpam-1854	66	6	(	(	PUNCT
ejpam-1854	66	7	1	1	X
ejpam-1854	66	8	)	)	PUNCT
ejpam-1854	66	9	α	α	PRON
ejpam-1854	66	10	∈	∈	PROPN
ejpam-1854	66	11	zp\z	zp\z	PUNCT
ejpam-1854	66	12	.	.	PUNCT
ejpam-1854	66	13	let	let	VERB
ejpam-1854	66	14	ε	ε	PROPN
ejpam-1854	66	15	>	>	X
ejpam-1854	66	16	0	0	PUNCT
ejpam-1854	66	17	be	be	AUX
ejpam-1854	66	18	an	an	DET
ejpam-1854	66	19	arbitrary	arbitrary	ADJ
ejpam-1854	66	20	real	real	ADJ
ejpam-1854	66	21	number	number	NOUN
ejpam-1854	66	22	.	.	PUNCT
ejpam-1854	67	1	then	then	ADV
ejpam-1854	67	2	,	,	PUNCT
ejpam-1854	67	3	0	0	X
ejpam-1854	67	4	<	<	X
ejpam-1854	67	5	�	�	PROPN
ejpam-1854	67	6	�	�	PROPN
ejpam-1854	67	7	α−	α−	ADP
ejpam-1854	67	8	sn	sn	PROPN
ejpam-1854	67	9	�	�	PROPN
ejpam-1854	67	10	�	�	PROPN
ejpam-1854	67	11	1	1	NUM
ejpam-1854	67	12	n	n	PROPN
ejpam-1854	67	13	p	p	NOUN
ejpam-1854	67	14	=	=	PUNCT
ejpam-1854	67	15	�	�	PROPN
ejpam-1854	67	16	�	�	PROPN
ejpam-1854	67	17	�	�	PROPN
ejpam-1854	67	18	�	�	PROPN
ejpam-1854	67	19	�	�	PROPN
ejpam-1854	67	20	∞	∞	PROPN
ejpam-1854	67	21	∑	∑	PROPN
ejpam-1854	67	22	i=1	i=1	PROPN
ejpam-1854	67	23	an+i	an+i	PROPN
ejpam-1854	67	24	�	�	PROPN
ejpam-1854	67	25	�	�	PROPN
ejpam-1854	67	26	�	�	PROPN
ejpam-1854	67	27	�	�	PROPN
ejpam-1854	67	28	�	�	PROPN
ejpam-1854	67	29	1	1	NUM
ejpam-1854	67	30	n	n	PROPN
ejpam-1854	67	31	p	p	NOUN
ejpam-1854	67	32	=	=	PUNCT
ejpam-1854	67	33	h	h	NOUN
ejpam-1854	67	34	max	max	PROPN
ejpam-1854	67	35	n	n	PROPN
ejpam-1854	67	36	�	�	PROPN
ejpam-1854	67	37	�	�	PROPN
ejpam-1854	67	38	an+1	an+1	NOUN
ejpam-1854	67	39	�	�	PROPN
ejpam-1854	67	40	�	�	PROPN
ejpam-1854	67	41	p	p	PROPN
ejpam-1854	67	42	,	,	PUNCT
ejpam-1854	67	43	�	�	PROPN
ejpam-1854	67	44	�	�	PROPN
ejpam-1854	67	45	an+2	an+2	PROPN
ejpam-1854	67	46	�	�	PROPN
ejpam-1854	67	47	�	�	PROPN
ejpam-1854	67	48	p	p	PROPN
ejpam-1854	67	49	,	,	PUNCT
ejpam-1854	67	50	.	.	PUNCT
ejpam-1854	67	51	.	.	PUNCT
ejpam-1854	67	52	.	.	PUNCT
ejpam-1854	68	1	oi	oi	INTJ
ejpam-1854	68	2	1	1	NUM
ejpam-1854	68	3	n	n	PROPN
ejpam-1854	68	4	h.	h.	PROPN
ejpam-1854	68	5	menken	menken	PROPN
ejpam-1854	68	6	,	,	PUNCT
ejpam-1854	68	7	a.	a.	PROPN
ejpam-1854	68	8	aşan	aşan	PROPN
ejpam-1854	68	9	/	/	SYM
ejpam-1854	68	10	eur	eur	PROPN
ejpam-1854	68	11	.	.	PUNCT
ejpam-1854	69	1	j.	j.	PROPN
ejpam-1854	69	2	pure	pure	PROPN
ejpam-1854	69	3	appl	appl	PROPN
ejpam-1854	69	4	.	.	PROPN
ejpam-1854	69	5	math	math	PROPN
ejpam-1854	69	6	,	,	PUNCT
ejpam-1854	69	7	6	6	NUM
ejpam-1854	69	8	(	(	PUNCT
ejpam-1854	69	9	2013	2013	NUM
ejpam-1854	69	10	)	)	PUNCT
ejpam-1854	69	11	,	,	PUNCT
ejpam-1854	69	12	239	239	NUM
ejpam-1854	69	13	-	-	SYM
ejpam-1854	69	14	246	246	NUM
ejpam-1854	69	15	242	242	NUM
ejpam-1854	69	16	where	where	SCONJ
ejpam-1854	69	17	sn	sn	PROPN
ejpam-1854	69	18	=	=	PUNCT
ejpam-1854	70	1	∑n	∑n	NOUN
ejpam-1854	70	2	i=1	i=1	PROPN
ejpam-1854	70	3	ai	ai	VERB
ejpam-1854	70	4	.	.	PUNCT
ejpam-1854	71	1	hence	hence	ADV
ejpam-1854	71	2	,	,	PUNCT
ejpam-1854	71	3	from	from	ADP
ejpam-1854	71	4	the	the	DET
ejpam-1854	71	5	condition	condition	NOUN
ejpam-1854	71	6	(	(	PUNCT
ejpam-1854	71	7	1	1	X
ejpam-1854	71	8	)	)	PUNCT
ejpam-1854	71	9	we	we	PRON
ejpam-1854	71	10	obtain	obtain	VERB
ejpam-1854	71	11	0	0	NUM
ejpam-1854	71	12	<	<	X
ejpam-1854	71	13	�	�	PROPN
ejpam-1854	71	14	�	�	PROPN
ejpam-1854	71	15	α−	α−	ADP
ejpam-1854	71	16	sn	sn	PROPN
ejpam-1854	71	17	�	�	PROPN
ejpam-1854	71	18	�	�	PROPN
ejpam-1854	71	19	1	1	NUM
ejpam-1854	71	20	n	n	PROPN
ejpam-1854	71	21	p	p	NOUN
ejpam-1854	71	22	=	=	PUNCT
ejpam-1854	71	23	�	�	PROPN
ejpam-1854	71	24	�	�	PROPN
ejpam-1854	71	25	an+1	an+1	NOUN
ejpam-1854	71	26	�	�	PROPN
ejpam-1854	71	27	�	�	PROPN
ejpam-1854	71	28	1	1	NUM
ejpam-1854	71	29	n	n	PROPN
ejpam-1854	71	30	p	p	NOUN
ejpam-1854	71	31	.	.	PUNCT
ejpam-1854	72	1	thus	thus	ADV
ejpam-1854	72	2	,	,	PUNCT
ejpam-1854	72	3	0	0	X
ejpam-1854	72	4	<	<	X
ejpam-1854	72	5	�	�	PROPN
ejpam-1854	72	6	�	�	PROPN
ejpam-1854	72	7	α−	α−	ADP
ejpam-1854	72	8	sn	sn	PROPN
ejpam-1854	72	9	�	�	PROPN
ejpam-1854	72	10	�	�	PROPN
ejpam-1854	72	11	1	1	NUM
ejpam-1854	72	12	n	n	PROPN
ejpam-1854	72	13	p	p	NOUN
ejpam-1854	72	14	=	=	NOUN
ejpam-1854	72	15	h	h	NOUN
ejpam-1854	72	16	p−νp(an+1	p−νp(an+1	NOUN
ejpam-1854	72	17	)	)	PUNCT
ejpam-1854	73	1	i	i	PRON
ejpam-1854	73	2	1	1	NUM
ejpam-1854	73	3	n	n	CCONJ
ejpam-1854	73	4	and	and	CCONJ
ejpam-1854	73	5	by	by	ADP
ejpam-1854	73	6	the	the	DET
ejpam-1854	73	7	inequality	inequality	NOUN
ejpam-1854	73	8	(	(	PUNCT
ejpam-1854	73	9	2	2	X
ejpam-1854	73	10	)	)	PUNCT
ejpam-1854	73	11	we	we	PRON
ejpam-1854	73	12	get	get	VERB
ejpam-1854	73	13	0	0	NUM
ejpam-1854	73	14	<	<	X
ejpam-1854	73	15	�	�	PROPN
ejpam-1854	73	16	�	�	PROPN
ejpam-1854	73	17	α−	α−	ADP
ejpam-1854	73	18	sn	sn	PROPN
ejpam-1854	73	19	�	�	PROPN
ejpam-1854	73	20	�	�	PROPN
ejpam-1854	73	21	1	1	NUM
ejpam-1854	73	22	n	n	PROPN
ejpam-1854	73	23	p	p	NOUN
ejpam-1854	73	24	=	=	NOUN
ejpam-1854	73	25	h	h	NOUN
ejpam-1854	73	26	p−νp(an+1	p−νp(an+1	NOUN
ejpam-1854	73	27	)	)	PUNCT
ejpam-1854	74	1	i	i	PRON
ejpam-1854	74	2	1	1	NUM
ejpam-1854	74	3	n	n	NOUN
ejpam-1854	74	4	≤	≤	NOUN
ejpam-1854	74	5	p−	p−	NOUN
ejpam-1854	74	6	n1+ε	n1+ε	NOUN
ejpam-1854	74	7	n	n	NOUN
ejpam-1854	74	8	=	=	SYM
ejpam-1854	74	9	p−nε	p−nε	PROPN
ejpam-1854	74	10	�	�	PROPN
ejpam-1854	74	11	n≥	n≥	PROPN
ejpam-1854	74	12	n0	n0	NUM
ejpam-1854	74	13	�	�	PROPN
ejpam-1854	74	14	.	.	PUNCT
ejpam-1854	75	1	thus	thus	ADV
ejpam-1854	75	2	we	we	PRON
ejpam-1854	75	3	have	have	VERB
ejpam-1854	75	4	�	�	PROPN
ejpam-1854	75	5	�	�	PROPN
ejpam-1854	75	6	α−	α−	ADP
ejpam-1854	75	7	sn	sn	PROPN
ejpam-1854	75	8	�	�	PROPN
ejpam-1854	75	9	�	�	PROPN
ejpam-1854	75	10	1	1	NUM
ejpam-1854	75	11	n	n	PROPN
ejpam-1854	75	12	p	p	X
ejpam-1854	75	13	→	→	X
ejpam-1854	75	14	0(n→∞	0(n→∞	NUM
ejpam-1854	75	15	)	)	PUNCT
ejpam-1854	75	16	.	.	PUNCT
ejpam-1854	76	1	since	since	SCONJ
ejpam-1854	76	2	sn	sn	PROPN
ejpam-1854	76	3	∈	∈	PROPN
ejpam-1854	76	4	zp	zp	PROPN
ejpam-1854	76	5	for	for	ADP
ejpam-1854	76	6	every	every	DET
ejpam-1854	76	7	n	n	PRON
ejpam-1854	76	8	∈	∈	PROPN
ejpam-1854	76	9	n	n	CCONJ
ejpam-1854	76	10	,	,	PUNCT
ejpam-1854	76	11	and	and	CCONJ
ejpam-1854	76	12	the	the	DET
ejpam-1854	76	13	set	set	NOUN
ejpam-1854	76	14	of	of	ADP
ejpam-1854	76	15	natural	natural	ADJ
ejpam-1854	76	16	numbers	number	NOUN
ejpam-1854	76	17	n	n	PRON
ejpam-1854	76	18	is	be	AUX
ejpam-1854	76	19	dense	dense	ADJ
ejpam-1854	76	20	in	in	ADP
ejpam-1854	76	21	zp	zp	PROPN
ejpam-1854	76	22	,	,	PUNCT
ejpam-1854	76	23	there	there	PRON
ejpam-1854	76	24	exists	exist	VERB
ejpam-1854	76	25	a	a	DET
ejpam-1854	76	26	sequence	sequence	NOUN
ejpam-1854	76	27	bn	bn	NOUN
ejpam-1854	76	28	from	from	ADP
ejpam-1854	76	29	n	n	CCONJ
ejpam-1854	76	30	such	such	ADJ
ejpam-1854	76	31	that	that	SCONJ
ejpam-1854	76	32	�	�	PROPN
ejpam-1854	76	33	�	�	PROPN
ejpam-1854	76	34	sn−	sn−	PROPN
ejpam-1854	76	35	bn	bn	PROPN
ejpam-1854	76	36	�	�	PROPN
ejpam-1854	76	37	�	�	PROPN
ejpam-1854	76	38	p	p	X
ejpam-1854	76	39	<	<	X
ejpam-1854	76	40	�	�	PROPN
ejpam-1854	76	41	�	�	PROPN
ejpam-1854	76	42	α−	α−	ADP
ejpam-1854	76	43	sn	sn	PROPN
ejpam-1854	76	44	�	�	PROPN
ejpam-1854	76	45	�	�	PROPN
ejpam-1854	76	46	p	p	PROPN
ejpam-1854	76	47	for	for	ADP
ejpam-1854	76	48	every	every	DET
ejpam-1854	76	49	n	n	CCONJ
ejpam-1854	76	50	∈	∈	NOUN
ejpam-1854	76	51	n.	n.	NOUN
ejpam-1854	76	52	by	by	ADP
ejpam-1854	76	53	the	the	DET
ejpam-1854	76	54	ultrametric	ultrametric	ADJ
ejpam-1854	76	55	inequality	inequality	NOUN
ejpam-1854	76	56	we	we	PRON
ejpam-1854	76	57	can	can	AUX
ejpam-1854	76	58	write	write	VERB
ejpam-1854	76	59	0	0	NUM
ejpam-1854	76	60	<	<	X
ejpam-1854	76	61	�	�	PROPN
ejpam-1854	76	62	�	�	PROPN
ejpam-1854	76	63	α−	α−	ADP
ejpam-1854	76	64	bn	bn	NOUN
ejpam-1854	76	65	�	�	PROPN
ejpam-1854	76	66	�	�	PROPN
ejpam-1854	76	67	p	p	PROPN
ejpam-1854	76	68	≤max	≤max	PROPN
ejpam-1854	76	69	n	n	PRON
ejpam-1854	76	70	�	�	PROPN
ejpam-1854	76	71	�	�	PROPN
ejpam-1854	76	72	α−	α−	ADP
ejpam-1854	76	73	sn	sn	PROPN
ejpam-1854	76	74	�	�	PROPN
ejpam-1854	76	75	�	�	PROPN
ejpam-1854	76	76	p	p	PROPN
ejpam-1854	76	77	,	,	PUNCT
ejpam-1854	76	78	�	�	PROPN
ejpam-1854	76	79	�	�	PROPN
ejpam-1854	76	80	sn−	sn−	PROPN
ejpam-1854	76	81	bn	bn	PROPN
ejpam-1854	76	82	�	�	PROPN
ejpam-1854	76	83	�	�	PROPN
ejpam-1854	76	84	p	p	NOUN
ejpam-1854	76	85	o	o	X
ejpam-1854	76	86	=	=	SYM
ejpam-1854	76	87	�	�	PROPN
ejpam-1854	76	88	�	�	PROPN
ejpam-1854	76	89	α−	α−	ADP
ejpam-1854	76	90	sn	sn	PROPN
ejpam-1854	76	91	�	�	PROPN
ejpam-1854	76	92	�	�	PROPN
ejpam-1854	76	93	p	p	PROPN
ejpam-1854	76	94	for	for	ADP
ejpam-1854	76	95	every	every	DET
ejpam-1854	76	96	n	n	CCONJ
ejpam-1854	76	97	∈	∈	PROPN
ejpam-1854	76	98	n.	n.	NOUN
ejpam-1854	76	99	hence	hence	ADV
ejpam-1854	76	100	,	,	PUNCT
ejpam-1854	76	101	we	we	PRON
ejpam-1854	76	102	can	can	AUX
ejpam-1854	76	103	obtain	obtain	VERB
ejpam-1854	76	104	a	a	DET
ejpam-1854	76	105	positive	positive	ADJ
ejpam-1854	76	106	integer	integer	NOUN
ejpam-1854	76	107	sequence	sequence	NOUN
ejpam-1854	76	108	bn	bn	ADP
ejpam-1854	76	109	such	such	ADJ
ejpam-1854	76	110	that	that	DET
ejpam-1854	76	111	0	0	NUM
ejpam-1854	76	112	<	<	X
ejpam-1854	76	113	�	�	PROPN
ejpam-1854	76	114	�	�	PROPN
ejpam-1854	76	115	α−	α−	ADP
ejpam-1854	76	116	bn	bn	NOUN
ejpam-1854	76	117	�	�	PROPN
ejpam-1854	76	118	�	�	PROPN
ejpam-1854	76	119	1	1	NUM
ejpam-1854	76	120	n	n	PROPN
ejpam-1854	76	121	p	p	PROPN
ejpam-1854	76	122	≤	≤	PROPN
ejpam-1854	76	123	�	�	PROPN
ejpam-1854	76	124	�	�	PROPN
ejpam-1854	76	125	α−	α−	ADP
ejpam-1854	76	126	sn	sn	PROPN
ejpam-1854	76	127	�	�	PROPN
ejpam-1854	76	128	�	�	PROPN
ejpam-1854	76	129	1	1	NUM
ejpam-1854	76	130	n	n	PROPN
ejpam-1854	76	131	p	p	NOUN
ejpam-1854	76	132	=	=	SYM
ejpam-1854	76	133	p−nε	p−nε	PROPN
ejpam-1854	76	134	→	→	SYM
ejpam-1854	76	135	0	0	NUM
ejpam-1854	76	136	(	(	PUNCT
ejpam-1854	76	137	n→∞	n→∞	NUM
ejpam-1854	76	138	)	)	PUNCT
ejpam-1854	76	139	.	.	PUNCT
ejpam-1854	77	1	so	so	ADV
ejpam-1854	77	2	,	,	PUNCT
ejpam-1854	77	3	the	the	DET
ejpam-1854	77	4	theorem	theorem	NOUN
ejpam-1854	77	5	is	be	AUX
ejpam-1854	77	6	proved	prove	VERB
ejpam-1854	77	7	.	.	PUNCT
ejpam-1854	78	1	remark	remark	PROPN
ejpam-1854	78	2	1	1	NUM
ejpam-1854	78	3	.	.	PUNCT
ejpam-1854	79	1	since	since	SCONJ
ejpam-1854	79	2	νp	νp	ADP
ejpam-1854	79	3	�	�	PROPN
ejpam-1854	79	4	an	an	DET
ejpam-1854	79	5	�	�	PROPN
ejpam-1854	79	6	∈	∈	PROPN
ejpam-1854	79	7	n	n	PROPN
ejpam-1854	79	8	for	for	ADP
ejpam-1854	79	9	all	all	DET
ejpam-1854	79	10	an	an	DET
ejpam-1854	79	11	∈	∈	PROPN
ejpam-1854	79	12	zp	zp	NOUN
ejpam-1854	79	13	,	,	PUNCT
ejpam-1854	79	14	in	in	ADP
ejpam-1854	79	15	theorem	theorem	NOUN
ejpam-1854	79	16	2	2	NUM
ejpam-1854	79	17	,	,	PUNCT
ejpam-1854	79	18	the	the	DET
ejpam-1854	79	19	condition	condition	NOUN
ejpam-1854	79	20	(	(	PUNCT
ejpam-1854	79	21	2	2	X
ejpam-1854	79	22	)	)	PUNCT
ejpam-1854	79	23	can	can	AUX
ejpam-1854	79	24	be	be	AUX
ejpam-1854	79	25	replaced	replace	VERB
ejpam-1854	79	26	by	by	ADP
ejpam-1854	79	27	the	the	DET
ejpam-1854	79	28	condition	condition	NOUN
ejpam-1854	79	29	νp	νp	ADP
ejpam-1854	79	30	�	�	PROPN
ejpam-1854	79	31	an+1	an+1	PROPN
ejpam-1854	79	32	�	�	PROPN
ejpam-1854	79	33	≥	≥	PROPN
ejpam-1854	79	34	n2	n2	PROPN
ejpam-1854	79	35	.	.	PUNCT
ejpam-1854	80	1	in	in	ADP
ejpam-1854	80	2	similar	similar	ADJ
ejpam-1854	80	3	way	way	NOUN
ejpam-1854	80	4	,	,	PUNCT
ejpam-1854	80	5	we	we	PRON
ejpam-1854	80	6	can	can	AUX
ejpam-1854	80	7	give	give	VERB
ejpam-1854	80	8	the	the	DET
ejpam-1854	80	9	following	follow	VERB
ejpam-1854	80	10	result	result	NOUN
ejpam-1854	80	11	.	.	PUNCT
ejpam-1854	81	1	corollary	corollary	ADJ
ejpam-1854	81	2	1	1	NUM
ejpam-1854	81	3	.	.	PUNCT
ejpam-1854	82	1	let	let	VERB
ejpam-1854	82	2	�	�	PROPN
ejpam-1854	82	3	an	an	DET
ejpam-1854	82	4	�	�	PROPN
ejpam-1854	82	5	be	be	AUX
ejpam-1854	82	6	a	a	DET
ejpam-1854	82	7	sequence	sequence	NOUN
ejpam-1854	82	8	of	of	ADP
ejpam-1854	82	9	positive	positive	ADJ
ejpam-1854	82	10	integers	integer	NOUN
ejpam-1854	82	11	such	such	ADJ
ejpam-1854	82	12	that	that	SCONJ
ejpam-1854	82	13	νp	νp	ADP
ejpam-1854	82	14	�	�	PROPN
ejpam-1854	82	15	an	an	DET
ejpam-1854	82	16	�	�	PROPN
ejpam-1854	82	17	<	<	X
ejpam-1854	82	18	νp	νp	PRON
ejpam-1854	82	19	�	�	PROPN
ejpam-1854	82	20	an+1	an+1	PROPN
ejpam-1854	82	21	�	�	PROPN
ejpam-1854	82	22	(	(	PUNCT
ejpam-1854	82	23	3	3	NUM
ejpam-1854	82	24	)	)	PUNCT
ejpam-1854	82	25	for	for	ADP
ejpam-1854	82	26	every	every	DET
ejpam-1854	82	27	n	n	CCONJ
ejpam-1854	82	28	,	,	PUNCT
ejpam-1854	82	29	and	and	CCONJ
ejpam-1854	82	30	νp	νp	DET
ejpam-1854	82	31	�	�	PROPN
ejpam-1854	82	32	an+1	an+1	PROPN
ejpam-1854	82	33	�	�	PROPN
ejpam-1854	82	34	≥	≥	PROPN
ejpam-1854	82	35	n2	n2	NOUN
ejpam-1854	82	36	(	(	PUNCT
ejpam-1854	82	37	4	4	NUM
ejpam-1854	82	38	)	)	PUNCT
ejpam-1854	82	39	for	for	ADP
ejpam-1854	82	40	n	n	CCONJ
ejpam-1854	82	41	>	>	X
ejpam-1854	82	42	n0	n0	PROPN
ejpam-1854	82	43	.	.	PUNCT
ejpam-1854	83	1	then	then	ADV
ejpam-1854	83	2	α=	α=	NUM
ejpam-1854	83	3	∞	∞	PROPN
ejpam-1854	83	4	∑	∑	PROPN
ejpam-1854	83	5	n=1	n=1	PROPN
ejpam-1854	83	6	an	an	PRON
ejpam-1854	83	7	is	be	AUX
ejpam-1854	83	8	a	a	DET
ejpam-1854	83	9	p	p	ADJ
ejpam-1854	83	10	-	-	PUNCT
ejpam-1854	83	11	adic	adic	ADJ
ejpam-1854	83	12	liouville	liouville	NOUN
ejpam-1854	83	13	number	number	NOUN
ejpam-1854	83	14	.	.	PUNCT
ejpam-1854	84	1	h.	h.	PROPN
ejpam-1854	84	2	menken	menken	PROPN
ejpam-1854	84	3	,	,	PUNCT
ejpam-1854	84	4	a.	a.	PROPN
ejpam-1854	84	5	aşan	aşan	PROPN
ejpam-1854	84	6	/	/	SYM
ejpam-1854	84	7	eur	eur	PROPN
ejpam-1854	84	8	.	.	PUNCT
ejpam-1854	85	1	j.	j.	PROPN
ejpam-1854	85	2	pure	pure	PROPN
ejpam-1854	85	3	appl	appl	PROPN
ejpam-1854	85	4	.	.	PROPN
ejpam-1854	85	5	math	math	PROPN
ejpam-1854	85	6	,	,	PUNCT
ejpam-1854	85	7	6	6	NUM
ejpam-1854	85	8	(	(	PUNCT
ejpam-1854	85	9	2013	2013	NUM
ejpam-1854	85	10	)	)	PUNCT
ejpam-1854	85	11	,	,	PUNCT
ejpam-1854	85	12	239	239	NUM
ejpam-1854	85	13	-	-	SYM
ejpam-1854	85	14	246	246	NUM
ejpam-1854	85	15	243	243	NUM
ejpam-1854	85	16	proof	proof	NOUN
ejpam-1854	85	17	.	.	PUNCT
ejpam-1854	86	1	by	by	ADP
ejpam-1854	86	2	the	the	DET
ejpam-1854	86	3	relations	relation	NOUN
ejpam-1854	86	4	(	(	PUNCT
ejpam-1854	86	5	3	3	NUM
ejpam-1854	86	6	)	)	PUNCT
ejpam-1854	86	7	and	and	CCONJ
ejpam-1854	86	8	(	(	PUNCT
ejpam-1854	86	9	4	4	X
ejpam-1854	86	10	)	)	PUNCT
ejpam-1854	86	11	we	we	PRON
ejpam-1854	86	12	have	have	VERB
ejpam-1854	86	13	,	,	PUNCT
ejpam-1854	86	14	l	l	PROPN
ejpam-1854	87	1	i	i	PRON
ejpam-1854	87	2	m	m	VERB
ejpam-1854	87	3	n→∞	n→∞	X
ejpam-1854	87	4	an	an	DET
ejpam-1854	87	5	=	=	NOUN
ejpam-1854	87	6	0	0	NUM
ejpam-1854	87	7	,	,	PUNCT
ejpam-1854	87	8	and	and	CCONJ
ejpam-1854	87	9	so	so	ADV
ejpam-1854	87	10	,	,	PUNCT
ejpam-1854	87	11	the	the	DET
ejpam-1854	87	12	series	series	PROPN
ejpam-1854	87	13	∑∞	∑∞	PROPN
ejpam-1854	87	14	n=1	n=1	PROPN
ejpam-1854	87	15	an	an	PRON
ejpam-1854	87	16	is	be	AUX
ejpam-1854	87	17	convergent	convergent	NOUN
ejpam-1854	87	18	and	and	CCONJ
ejpam-1854	88	1	α	α	PRON
ejpam-1854	88	2	∈	∈	PROPN
ejpam-1854	88	3	zp	zp	PROPN
ejpam-1854	88	4	.	.	PROPN
ejpam-1854	88	5	similarly	similarly	ADV
ejpam-1854	88	6	,	,	PUNCT
ejpam-1854	88	7	we	we	PRON
ejpam-1854	88	8	can	can	AUX
ejpam-1854	88	9	obtain	obtain	VERB
ejpam-1854	88	10	that	that	PRON
ejpam-1854	88	11	0	0	NUM
ejpam-1854	88	12	<	<	X
ejpam-1854	88	13	�	�	PROPN
ejpam-1854	88	14	�	�	PROPN
ejpam-1854	88	15	α−	α−	ADP
ejpam-1854	88	16	sn	sn	PROPN
ejpam-1854	88	17	�	�	PROPN
ejpam-1854	88	18	�	�	PROPN
ejpam-1854	88	19	1	1	NUM
ejpam-1854	88	20	n	n	PROPN
ejpam-1854	88	21	p	p	NOUN
ejpam-1854	88	22	=	=	NOUN
ejpam-1854	88	23	h	h	NOUN
ejpam-1854	88	24	p−νp(an+1	p−νp(an+1	NOUN
ejpam-1854	88	25	)	)	PUNCT
ejpam-1854	89	1	i	i	PRON
ejpam-1854	89	2	1	1	NUM
ejpam-1854	89	3	n	n	NOUN
ejpam-1854	89	4	≤	≤	NOUN
ejpam-1854	89	5	p−	p−	NOUN
ejpam-1854	89	6	n2	n2	NOUN
ejpam-1854	89	7	n	n	PROPN
ejpam-1854	89	8	=	=	PROPN
ejpam-1854	89	9	p−n→	p−n→	PROPN
ejpam-1854	89	10	0	0	NUM
ejpam-1854	89	11	(	(	PUNCT
ejpam-1854	89	12	n→∞	n→∞	NUM
ejpam-1854	89	13	)	)	PUNCT
ejpam-1854	90	1	where	where	SCONJ
ejpam-1854	90	2	sn	sn	PROPN
ejpam-1854	90	3	=	=	PUNCT
ejpam-1854	90	4	∑n	∑n	NOUN
ejpam-1854	90	5	i=1	i=1	PROPN
ejpam-1854	90	6	ai	ai	VERB
ejpam-1854	90	7	.	.	PUNCT
ejpam-1854	91	1	also	also	ADV
ejpam-1854	91	2	,	,	PUNCT
ejpam-1854	91	3	since	since	SCONJ
ejpam-1854	91	4	sn	sn	PROPN
ejpam-1854	91	5	∈	∈	PROPN
ejpam-1854	91	6	n	n	INTJ
ejpam-1854	91	7	for	for	ADP
ejpam-1854	91	8	all	all	DET
ejpam-1854	91	9	n	n	PRON
ejpam-1854	91	10	∈	∈	PROPN
ejpam-1854	91	11	n	n	CCONJ
ejpam-1854	91	12	,	,	PUNCT
ejpam-1854	91	13	the	the	DET
ejpam-1854	91	14	number	number	NOUN
ejpam-1854	91	15	α	α	NOUN
ejpam-1854	91	16	is	be	AUX
ejpam-1854	91	17	a	a	DET
ejpam-1854	91	18	p	p	ADJ
ejpam-1854	91	19	-	-	PUNCT
ejpam-1854	91	20	adic	adic	ADJ
ejpam-1854	91	21	liouville	liouville	NOUN
ejpam-1854	91	22	number	number	NOUN
ejpam-1854	91	23	.	.	PUNCT
ejpam-1854	92	1	3	3	X
ejpam-1854	92	2	.	.	X
ejpam-1854	92	3	the	the	DET
ejpam-1854	92	4	erdös	erdös	PROPN
ejpam-1854	92	5	theorem	theorem	NOUN
ejpam-1854	92	6	in	in	ADP
ejpam-1854	92	7	the	the	DET
ejpam-1854	92	8	functions	function	NOUN
ejpam-1854	92	9	field	field	NOUN
ejpam-1854	92	10	k	k	PROPN
ejpam-1854	92	11	〈	〈	PROPN
ejpam-1854	92	12	x	x	X
ejpam-1854	92	13	〉	〉	NOUN
ejpam-1854	92	14	let	let	VERB
ejpam-1854	92	15	k	k	PROPN
ejpam-1854	92	16	be	be	AUX
ejpam-1854	92	17	an	an	DET
ejpam-1854	92	18	arbitrary	arbitrary	ADJ
ejpam-1854	92	19	field	field	NOUN
ejpam-1854	92	20	,	,	PUNCT
ejpam-1854	92	21	x	x	PUNCT
ejpam-1854	92	22	an	an	DET
ejpam-1854	92	23	indeterminate	indeterminate	NOUN
ejpam-1854	92	24	,	,	PUNCT
ejpam-1854	92	25	k	k	PROPN
ejpam-1854	93	1	[	[	X
ejpam-1854	93	2	x	x	X
ejpam-1854	93	3	]	]	X
ejpam-1854	93	4	the	the	DET
ejpam-1854	93	5	ring	ring	NOUN
ejpam-1854	93	6	of	of	ADP
ejpam-1854	93	7	all	all	DET
ejpam-1854	93	8	polynomials	polynomial	NOUN
ejpam-1854	93	9	in	in	ADP
ejpam-1854	93	10	x	x	PUNCT
ejpam-1854	93	11	with	with	ADP
ejpam-1854	93	12	coefficients	coefficient	NOUN
ejpam-1854	93	13	in	in	ADP
ejpam-1854	93	14	k	k	PROPN
ejpam-1854	93	15	,	,	PUNCT
ejpam-1854	93	16	k	k	PROPN
ejpam-1854	93	17	(	(	PUNCT
ejpam-1854	93	18	x	x	X
ejpam-1854	93	19	)	)	PUNCT
ejpam-1854	93	20	the	the	DET
ejpam-1854	93	21	field	field	NOUN
ejpam-1854	93	22	of	of	ADP
ejpam-1854	93	23	all	all	DET
ejpam-1854	93	24	rational	rational	ADJ
ejpam-1854	93	25	functions	function	NOUN
ejpam-1854	93	26	in	in	ADP
ejpam-1854	93	27	x	x	PUNCT
ejpam-1854	93	28	with	with	ADP
ejpam-1854	93	29	coefficients	coefficient	NOUN
ejpam-1854	93	30	in	in	ADP
ejpam-1854	93	31	k	k	PROPN
ejpam-1854	93	32	,	,	PUNCT
ejpam-1854	93	33	and	and	CCONJ
ejpam-1854	93	34	k	k	PROPN
ejpam-1854	93	35	〈	〈	PROPN
ejpam-1854	93	36	x	x	X
ejpam-1854	93	37	〉	〉	NOUN
ejpam-1854	93	38	the	the	DET
ejpam-1854	93	39	field	field	NOUN
ejpam-1854	93	40	of	of	ADP
ejpam-1854	93	41	all	all	DET
ejpam-1854	93	42	formal	formal	ADJ
ejpam-1854	93	43	series	series	NOUN
ejpam-1854	93	44	z	z	PROPN
ejpam-1854	93	45	=	=	SYM
ejpam-1854	93	46	ak	ak	PROPN
ejpam-1854	93	47	xk	xk	PROPN
ejpam-1854	93	48	+	+	PROPN
ejpam-1854	93	49	ak−1	ak−1	PROPN
ejpam-1854	93	50	xk−1	xk−1	PROPN
ejpam-1854	93	51	+	+	PROPN
ejpam-1854	93	52	ak−2	ak−2	PROPN
ejpam-1854	93	53	xk−2	xk−2	PROPN
ejpam-1854	93	54	+	+	PROPN
ejpam-1854	93	55	.	.	PUNCT
ejpam-1854	93	56	.	.	PUNCT
ejpam-1854	93	57	.	.	PUNCT
ejpam-1854	94	1	in	in	ADP
ejpam-1854	94	2	x	x	SYM
ejpam-1854	94	3	where	where	SCONJ
ejpam-1854	94	4	the	the	DET
ejpam-1854	94	5	coefficients	coefficient	NOUN
ejpam-1854	94	6	ak	ak	PROPN
ejpam-1854	94	7	,	,	PUNCT
ejpam-1854	94	8	ak−1	ak−1	PROPN
ejpam-1854	94	9	,	,	PUNCT
ejpam-1854	94	10	ak−2	ak−2	PROPN
ejpam-1854	94	11	,	,	PUNCT
ejpam-1854	94	12	.	.	PUNCT
ejpam-1854	94	13	.	.	PUNCT
ejpam-1854	94	14	.	.	PUNCT
ejpam-1854	95	1	are	be	AUX
ejpam-1854	95	2	in	in	ADP
ejpam-1854	95	3	k	k	PROPN
ejpam-1854	95	4	.	.	PUNCT
ejpam-1854	96	1	thus	thus	ADV
ejpam-1854	96	2	k	k	X
ejpam-1854	96	3	(	(	PUNCT
ejpam-1854	96	4	x	x	X
ejpam-1854	96	5	)	)	PUNCT
ejpam-1854	96	6	is	be	AUX
ejpam-1854	96	7	the	the	DET
ejpam-1854	96	8	quotient	quotient	NOUN
ejpam-1854	96	9	field	field	NOUN
ejpam-1854	96	10	of	of	ADP
ejpam-1854	96	11	k	k	PROPN
ejpam-1854	96	12	[	[	X
ejpam-1854	96	13	x	x	X
ejpam-1854	96	14	]	]	X
ejpam-1854	96	15	and	and	CCONJ
ejpam-1854	96	16	a	a	DET
ejpam-1854	96	17	subfield	subfield	NOUN
ejpam-1854	96	18	of	of	ADP
ejpam-1854	96	19	k	k	PROPN
ejpam-1854	96	20	〈	〈	PROPN
ejpam-1854	96	21	x	x	X
ejpam-1854	96	22	〉	〉	NOUN
ejpam-1854	96	23	.	.	PUNCT
ejpam-1854	97	1	a	a	DET
ejpam-1854	97	2	valuation	valuation	NOUN
ejpam-1854	97	3	|z|	|z|	NOUN
ejpam-1854	97	4	in	in	ADP
ejpam-1854	97	5	k	k	PROPN
ejpam-1854	97	6	〈	〈	PROPN
ejpam-1854	97	7	x	x	NOUN
ejpam-1854	97	8	〉	〉	NOUN
ejpam-1854	97	9	is	be	AUX
ejpam-1854	97	10	now	now	ADV
ejpam-1854	97	11	defined	define	VERB
ejpam-1854	97	12	by	by	ADP
ejpam-1854	97	13	putting	put	VERB
ejpam-1854	97	14	|0|=	|0|=	PROPN
ejpam-1854	97	15	0	0	NUM
ejpam-1854	97	16	;	;	PUNCT
ejpam-1854	97	17	but	but	CCONJ
ejpam-1854	97	18	|z|=	|z|=	NOUN
ejpam-1854	97	19	ek	ek	VERB
ejpam-1854	98	1	if	if	SCONJ
ejpam-1854	98	2	z	z	NOUN
ejpam-1854	98	3	=	=	SYM
ejpam-1854	98	4	ak	ak	PROPN
ejpam-1854	98	5	xk	xk	PROPN
ejpam-1854	98	6	+	+	PROPN
ejpam-1854	98	7	ak−1	ak−1	PROPN
ejpam-1854	98	8	xk−1	xk−1	PROPN
ejpam-1854	98	9	+	+	PROPN
ejpam-1854	98	10	ak−2	ak−2	PROPN
ejpam-1854	98	11	xk−2	xk−2	PROPN
ejpam-1854	98	12	+	+	PROPN
ejpam-1854	98	13	.	.	PUNCT
ejpam-1854	98	14	.	.	PUNCT
ejpam-1854	98	15	.	.	PUNCT
ejpam-1854	99	1	and	and	CCONJ
ejpam-1854	99	2	ak	ak	PROPN
ejpam-1854	99	3	6=	6=	PROPN
ejpam-1854	99	4	0	0	NUM
ejpam-1854	99	5	.	.	PUNCT
ejpam-1854	100	1	if	if	SCONJ
ejpam-1854	100	2	z	z	NOUN
ejpam-1854	100	3	lies	lie	VERB
ejpam-1854	100	4	in	in	ADP
ejpam-1854	100	5	k	k	PROPN
ejpam-1854	101	1	[	[	X
ejpam-1854	101	2	x	x	X
ejpam-1854	101	3	]	]	X
ejpam-1854	101	4	,	,	PUNCT
ejpam-1854	101	5	then	then	ADV
ejpam-1854	101	6	log	log	PROPN
ejpam-1854	101	7	|z|=	|z|=	NOUN
ejpam-1854	101	8	deg	deg	PROPN
ejpam-1854	102	1	z.	z.	PROPN
ejpam-1854	103	1	it	it	PRON
ejpam-1854	103	2	is	be	AUX
ejpam-1854	103	3	clear	clear	ADJ
ejpam-1854	103	4	that	that	SCONJ
ejpam-1854	103	5	this	this	DET
ejpam-1854	103	6	norm	norm	NOUN
ejpam-1854	103	7	is	be	AUX
ejpam-1854	103	8	a	a	DET
ejpam-1854	103	9	non	non	ADJ
ejpam-1854	103	10	-	-	ADJ
ejpam-1854	103	11	archimedean	archimedean	ADJ
ejpam-1854	103	12	and	and	CCONJ
ejpam-1854	103	13	so	so	ADV
ejpam-1854	103	14	,	,	PUNCT
ejpam-1854	103	15	k	k	PROPN
ejpam-1854	103	16	〈	〈	PROPN
ejpam-1854	103	17	x	x	X
ejpam-1854	103	18	〉	〉	NOUN
ejpam-1854	103	19	is	be	AUX
ejpam-1854	103	20	a	a	DET
ejpam-1854	103	21	non	non	ADJ
ejpam-1854	103	22	-	-	ADJ
ejpam-1854	103	23	archimedean	archimedean	ADJ
ejpam-1854	103	24	field	field	NOUN
ejpam-1854	103	25	with	with	ADP
ejpam-1854	103	26	this	this	DET
ejpam-1854	103	27	norm	norm	NOUN
ejpam-1854	103	28	.	.	PUNCT
ejpam-1854	104	1	the	the	DET
ejpam-1854	104	2	analogue	analogue	NOUN
ejpam-1854	104	3	of	of	ADP
ejpam-1854	104	4	liouville	liouville	PROPN
ejpam-1854	104	5	’s	’s	PART
ejpam-1854	104	6	theorem	theorem	ADJ
ejpam-1854	104	7	states	state	NOUN
ejpam-1854	104	8	that	that	SCONJ
ejpam-1854	104	9	if	if	SCONJ
ejpam-1854	104	10	α	α	PROPN
ejpam-1854	104	11	∈	∈	X
ejpam-1854	104	12	k	k	X
ejpam-1854	104	13	〈	〈	PROPN
ejpam-1854	104	14	x	x	NOUN
ejpam-1854	104	15	〉	〉	NOUN
ejpam-1854	104	16	is	be	AUX
ejpam-1854	104	17	an	an	DET
ejpam-1854	104	18	algebraic	algebraic	ADJ
ejpam-1854	104	19	number	number	NOUN
ejpam-1854	104	20	of	of	ADP
ejpam-1854	104	21	degree	degree	NOUN
ejpam-1854	104	22	n	n	PRON
ejpam-1854	104	23	≥	≥	NOUN
ejpam-1854	104	24	2	2	NUM
ejpam-1854	104	25	over	over	ADP
ejpam-1854	104	26	k(x	k(x	PROPN
ejpam-1854	104	27	)	)	PUNCT
ejpam-1854	104	28	,	,	PUNCT
ejpam-1854	104	29	then	then	ADV
ejpam-1854	104	30	there	there	PRON
ejpam-1854	104	31	exists	exist	VERB
ejpam-1854	104	32	a	a	DET
ejpam-1854	104	33	positive	positive	ADJ
ejpam-1854	104	34	constant	constant	ADJ
ejpam-1854	104	35	c(α	c(α	NOUN
ejpam-1854	104	36	)	)	PUNCT
ejpam-1854	104	37	depending	depend	VERB
ejpam-1854	104	38	only	only	ADV
ejpam-1854	104	39	on	on	ADP
ejpam-1854	104	40	α	α	PRON
ejpam-1854	104	41	such	such	ADJ
ejpam-1854	104	42	that	that	SCONJ
ejpam-1854	104	43	�	�	PROPN
ejpam-1854	104	44	�	�	PROPN
ejpam-1854	104	45	�	�	PROPN
ejpam-1854	104	46	α−	α−	ADP
ejpam-1854	104	47	a	a	DET
ejpam-1854	104	48	b	b	PROPN
ejpam-1854	104	49	�	�	PROPN
ejpam-1854	104	50	�	�	PROPN
ejpam-1854	104	51	�	�	PROPN
ejpam-1854	104	52	≥	≥	PROPN
ejpam-1854	104	53	c(α	c(α	NOUN
ejpam-1854	104	54	)	)	PUNCT
ejpam-1854	104	55	bn	bn	ADP
ejpam-1854	104	56	for	for	ADP
ejpam-1854	104	57	all	all	DET
ejpam-1854	104	58	a	a	PRON
ejpam-1854	104	59	,	,	PUNCT
ejpam-1854	104	60	b	b	X
ejpam-1854	104	61	∈	∈	ADP
ejpam-1854	104	62	k	k	X
ejpam-1854	105	1	[	[	X
ejpam-1854	105	2	x	x	X
ejpam-1854	105	3	]	]	X
ejpam-1854	105	4	(	(	PUNCT
ejpam-1854	105	5	b	b	PROPN
ejpam-1854	105	6	6=	6=	NUM
ejpam-1854	105	7	0	0	NUM
ejpam-1854	105	8	)	)	PUNCT
ejpam-1854	106	1	[	[	X
ejpam-1854	106	2	see	see	VERB
ejpam-1854	106	3	16	16	NUM
ejpam-1854	106	4	]	]	PUNCT
ejpam-1854	106	5	.	.	PUNCT
ejpam-1854	107	1	some	some	DET
ejpam-1854	107	2	investigations	investigation	NOUN
ejpam-1854	107	3	involve	involve	VERB
ejpam-1854	107	4	the	the	DET
ejpam-1854	107	5	liouville	liouville	NOUN
ejpam-1854	107	6	numbers	number	NOUN
ejpam-1854	107	7	in	in	ADP
ejpam-1854	107	8	the	the	DET
ejpam-1854	107	9	functions	function	NOUN
ejpam-1854	107	10	field	field	NOUN
ejpam-1854	107	11	was	be	AUX
ejpam-1854	107	12	done	do	VERB
ejpam-1854	107	13	in	in	ADP
ejpam-1854	107	14	[	[	X
ejpam-1854	107	15	11	11	NUM
ejpam-1854	107	16	]	]	PUNCT
ejpam-1854	107	17	.	.	PUNCT
ejpam-1854	108	1	now	now	ADV
ejpam-1854	108	2	we	we	PRON
ejpam-1854	108	3	recall	recall	VERB
ejpam-1854	108	4	the	the	DET
ejpam-1854	108	5	definition	definition	NOUN
ejpam-1854	108	6	of	of	ADP
ejpam-1854	108	7	liouville	liouville	NOUN
ejpam-1854	108	8	numbers	number	NOUN
ejpam-1854	108	9	in	in	ADP
ejpam-1854	108	10	this	this	DET
ejpam-1854	108	11	field	field	NOUN
ejpam-1854	108	12	.	.	PUNCT
ejpam-1854	109	1	definition	definition	NOUN
ejpam-1854	109	2	2	2	NUM
ejpam-1854	109	3	.	.	PUNCT
ejpam-1854	110	1	an	an	DET
ejpam-1854	110	2	element	element	NOUN
ejpam-1854	110	3	ξ	ξ	PROPN
ejpam-1854	110	4	∈	∈	PROPN
ejpam-1854	110	5	k	k	X
ejpam-1854	110	6	〈	〈	PROPN
ejpam-1854	110	7	x	x	NOUN
ejpam-1854	110	8	〉	〉	NOUN
ejpam-1854	110	9	is	be	AUX
ejpam-1854	110	10	called	call	VERB
ejpam-1854	110	11	a	a	DET
ejpam-1854	110	12	liouville	liouville	NOUN
ejpam-1854	110	13	number	number	NOUN
ejpam-1854	110	14	if	if	SCONJ
ejpam-1854	110	15	for	for	ADP
ejpam-1854	110	16	every	every	DET
ejpam-1854	110	17	ω	ω	PROPN
ejpam-1854	110	18	∈	∈	PROPN
ejpam-1854	110	19	r+	r+	NOUN
ejpam-1854	110	20	,	,	PUNCT
ejpam-1854	110	21	there	there	PRON
ejpam-1854	110	22	exist	exist	VERB
ejpam-1854	110	23	integer	integer	NOUN
ejpam-1854	110	24	a	a	PRON
ejpam-1854	110	25	,	,	PUNCT
ejpam-1854	110	26	b	b	PROPN
ejpam-1854	110	27	∈	∈	PROPN
ejpam-1854	110	28	k	k	X
ejpam-1854	111	1	[	[	X
ejpam-1854	111	2	x]\{0	x]\{0	ADV
ejpam-1854	111	3	}	}	PUNCT
ejpam-1854	111	4	with	with	ADP
ejpam-1854	111	5	|b|	|b|	PROPN
ejpam-1854	111	6	>	>	X
ejpam-1854	111	7	1	1	NUM
ejpam-1854	111	8	such	such	ADJ
ejpam-1854	111	9	that	that	SCONJ
ejpam-1854	111	10	0	0	NUM
ejpam-1854	111	11	<	<	X
ejpam-1854	111	12	�	�	PROPN
ejpam-1854	111	13	�	�	PROPN
ejpam-1854	111	14	�	�	PROPN
ejpam-1854	111	15	ξ−	ξ−	PROPN
ejpam-1854	111	16	a	a	DET
ejpam-1854	111	17	b	b	PROPN
ejpam-1854	111	18	�	�	PROPN
ejpam-1854	111	19	�	�	PROPN
ejpam-1854	111	20	�	�	PROPN
ejpam-1854	111	21	<	<	X
ejpam-1854	111	22	1	1	NUM
ejpam-1854	111	23	bω	bω	NOUN
ejpam-1854	111	24	.	.	PUNCT
ejpam-1854	112	1	we	we	PRON
ejpam-1854	112	2	can	can	AUX
ejpam-1854	112	3	give	give	VERB
ejpam-1854	112	4	an	an	DET
ejpam-1854	112	5	analogue	analogue	NOUN
ejpam-1854	112	6	of	of	ADP
ejpam-1854	112	7	the	the	DET
ejpam-1854	112	8	erdös	erdös	PROPN
ejpam-1854	112	9	theorem	theorem	NOUN
ejpam-1854	112	10	in	in	ADP
ejpam-1854	112	11	the	the	DET
ejpam-1854	112	12	functions	function	NOUN
ejpam-1854	112	13	field	field	NOUN
ejpam-1854	112	14	as	as	SCONJ
ejpam-1854	112	15	follows	follow	VERB
ejpam-1854	112	16	h.	h.	PROPN
ejpam-1854	112	17	menken	menken	PROPN
ejpam-1854	112	18	,	,	PUNCT
ejpam-1854	112	19	a.	a.	PROPN
ejpam-1854	112	20	aşan	aşan	PROPN
ejpam-1854	112	21	/	/	SYM
ejpam-1854	112	22	eur	eur	PROPN
ejpam-1854	112	23	.	.	PUNCT
ejpam-1854	113	1	j.	j.	PROPN
ejpam-1854	113	2	pure	pure	PROPN
ejpam-1854	113	3	appl	appl	PROPN
ejpam-1854	113	4	.	.	PROPN
ejpam-1854	113	5	math	math	PROPN
ejpam-1854	113	6	,	,	PUNCT
ejpam-1854	113	7	6	6	NUM
ejpam-1854	113	8	(	(	PUNCT
ejpam-1854	113	9	2013	2013	NUM
ejpam-1854	113	10	)	)	PUNCT
ejpam-1854	113	11	,	,	PUNCT
ejpam-1854	113	12	239	239	NUM
ejpam-1854	113	13	-	-	SYM
ejpam-1854	113	14	246	246	NUM
ejpam-1854	113	15	244	244	NUM
ejpam-1854	113	16	theorem	theorem	NOUN
ejpam-1854	113	17	3	3	X
ejpam-1854	113	18	.	.	PUNCT
ejpam-1854	114	1	let	let	VERB
ejpam-1854	114	2	�	�	PROPN
ejpam-1854	114	3	zn	zn	PROPN
ejpam-1854	114	4	�	�	PROPN
ejpam-1854	114	5	be	be	AUX
ejpam-1854	114	6	a	a	DET
ejpam-1854	114	7	sequence	sequence	NOUN
ejpam-1854	114	8	of	of	ADP
ejpam-1854	114	9	formal	formal	ADJ
ejpam-1854	114	10	series	series	NOUN
ejpam-1854	114	11	in	in	ADP
ejpam-1854	114	12	k	k	PROPN
ejpam-1854	114	13	〈	〈	PROPN
ejpam-1854	114	14	x	x	X
ejpam-1854	114	15	〉	〉	NOUN
ejpam-1854	114	16	such	such	ADJ
ejpam-1854	114	17	that	that	SCONJ
ejpam-1854	114	18	deg	deg	PROPN
ejpam-1854	114	19	�	�	PROPN
ejpam-1854	114	20	zn+1	zn+1	PROPN
ejpam-1854	114	21	�	�	PROPN
ejpam-1854	114	22	<	<	X
ejpam-1854	114	23	deg	deg	PROPN
ejpam-1854	114	24	�	�	PROPN
ejpam-1854	114	25	zn	zn	PROPN
ejpam-1854	114	26	�	�	PROPN
ejpam-1854	114	27	<	<	X
ejpam-1854	114	28	0	0	PUNCT
ejpam-1854	114	29	(	(	PUNCT
ejpam-1854	114	30	5	5	NUM
ejpam-1854	114	31	)	)	PUNCT
ejpam-1854	114	32	for	for	ADP
ejpam-1854	114	33	every	every	DET
ejpam-1854	114	34	n	n	NOUN
ejpam-1854	114	35	and	and	CCONJ
ejpam-1854	114	36	deg	deg	PROPN
ejpam-1854	114	37	�	�	PROPN
ejpam-1854	114	38	zn+1	zn+1	PROPN
ejpam-1854	114	39	�	�	PROPN
ejpam-1854	114	40	≤−n1+ε	≤−n1+ε	PROPN
ejpam-1854	114	41	(	(	PUNCT
ejpam-1854	114	42	6	6	NUM
ejpam-1854	114	43	)	)	PUNCT
ejpam-1854	114	44	for	for	ADP
ejpam-1854	114	45	fixed	fix	VERB
ejpam-1854	114	46	ε	ε	PROPN
ejpam-1854	114	47	>	>	X
ejpam-1854	114	48	0	0	PROPN
ejpam-1854	114	49	and	and	CCONJ
ejpam-1854	114	50	n	n	CCONJ
ejpam-1854	114	51	>	>	X
ejpam-1854	114	52	n0	n0	X
ejpam-1854	114	53	(	(	PUNCT
ejpam-1854	114	54	ε	ε	PROPN
ejpam-1854	114	55	)	)	PUNCT
ejpam-1854	114	56	.	.	PUNCT
ejpam-1854	115	1	then	then	ADV
ejpam-1854	115	2	,	,	PUNCT
ejpam-1854	115	3	α=	α=	ADJ
ejpam-1854	115	4	∞	∞	NUM
ejpam-1854	115	5	∑	∑	PROPN
ejpam-1854	115	6	n=1	n=1	PROPN
ejpam-1854	115	7	zn	zn	PROPN
ejpam-1854	115	8	is	be	AUX
ejpam-1854	115	9	a	a	DET
ejpam-1854	115	10	liouville	liouville	NOUN
ejpam-1854	115	11	number	number	NOUN
ejpam-1854	115	12	in	in	ADP
ejpam-1854	115	13	k	k	PROPN
ejpam-1854	115	14	〈	〈	PROPN
ejpam-1854	115	15	x	x	X
ejpam-1854	115	16	〉	〉	NOUN
ejpam-1854	115	17	.	.	PUNCT
ejpam-1854	116	1	proof	proof	NOUN
ejpam-1854	116	2	.	.	PUNCT
ejpam-1854	117	1	first	first	ADV
ejpam-1854	117	2	we	we	PRON
ejpam-1854	117	3	show	show	VERB
ejpam-1854	117	4	that	that	SCONJ
ejpam-1854	117	5	the	the	DET
ejpam-1854	117	6	series	series	PROPN
ejpam-1854	117	7	∑∞	∑∞	PROPN
ejpam-1854	117	8	n=1	n=1	PROPN
ejpam-1854	117	9	zn	zn	PROPN
ejpam-1854	117	10	is	be	AUX
ejpam-1854	117	11	convergent	convergent	ADJ
ejpam-1854	117	12	.	.	PUNCT
ejpam-1854	118	1	it	it	PRON
ejpam-1854	118	2	follows	follow	VERB
ejpam-1854	118	3	from	from	ADP
ejpam-1854	118	4	the	the	DET
ejpam-1854	118	5	condition	condition	NOUN
ejpam-1854	118	6	(	(	PUNCT
ejpam-1854	118	7	6	6	NUM
ejpam-1854	118	8	)	)	PUNCT
ejpam-1854	118	9	that	that	PRON
ejpam-1854	118	10	�	�	PROPN
ejpam-1854	118	11	�	�	PROPN
ejpam-1854	118	12	zn+1	zn+1	PROPN
ejpam-1854	118	13	�	�	PROPN
ejpam-1854	118	14	�	�	PROPN
ejpam-1854	118	15	=	=	SYM
ejpam-1854	118	16	edeg(zn+1	edeg(zn+1	PROPN
ejpam-1854	118	17	)	)	PUNCT
ejpam-1854	118	18	≤	≤	NOUN
ejpam-1854	118	19	e−n1+ε	e−n1+ε	NOUN
ejpam-1854	118	20	for	for	ADP
ejpam-1854	118	21	fixed	fix	VERB
ejpam-1854	118	22	ε	ε	PROPN
ejpam-1854	118	23	>	>	X
ejpam-1854	118	24	0	0	PROPN
ejpam-1854	118	25	and	and	CCONJ
ejpam-1854	118	26	n	n	CCONJ
ejpam-1854	118	27	>	>	X
ejpam-1854	118	28	n0	n0	X
ejpam-1854	118	29	(	(	PUNCT
ejpam-1854	118	30	ε	ε	PROPN
ejpam-1854	118	31	)	)	PUNCT
ejpam-1854	118	32	.	.	PUNCT
ejpam-1854	119	1	then	then	ADV
ejpam-1854	119	2	,	,	PUNCT
ejpam-1854	119	3	we	we	PRON
ejpam-1854	119	4	get	get	VERB
ejpam-1854	119	5	l	l	PROPN
ejpam-1854	120	1	i	i	PRON
ejpam-1854	120	2	m	m	VERB
ejpam-1854	120	3	n→∞	n→∞	X
ejpam-1854	120	4	zn	zn	NOUN
ejpam-1854	120	5	=	=	SYM
ejpam-1854	120	6	0	0	PROPN
ejpam-1854	120	7	.	.	PUNCT
ejpam-1854	121	1	thus	thus	ADV
ejpam-1854	121	2	,	,	PUNCT
ejpam-1854	121	3	the	the	DET
ejpam-1854	121	4	series	series	PROPN
ejpam-1854	121	5	∑∞	∑∞	PROPN
ejpam-1854	121	6	n=1	n=1	PROPN
ejpam-1854	121	7	zn	zn	PROPN
ejpam-1854	121	8	is	be	AUX
ejpam-1854	121	9	convergent	convergent	ADJ
ejpam-1854	121	10	.	.	PUNCT
ejpam-1854	122	1	let	let	VERB
ejpam-1854	122	2	ε	ε	PROPN
ejpam-1854	122	3	>	>	X
ejpam-1854	122	4	0	0	PUNCT
ejpam-1854	122	5	be	be	AUX
ejpam-1854	122	6	an	an	DET
ejpam-1854	122	7	arbitrary	arbitrary	ADJ
ejpam-1854	122	8	real	real	ADJ
ejpam-1854	122	9	number	number	NOUN
ejpam-1854	122	10	.	.	PUNCT
ejpam-1854	123	1	then	then	ADV
ejpam-1854	123	2	,	,	PUNCT
ejpam-1854	123	3	0	0	X
ejpam-1854	123	4	<	<	X
ejpam-1854	123	5	�	�	PROPN
ejpam-1854	123	6	�	�	PROPN
ejpam-1854	123	7	α−	α−	ADP
ejpam-1854	123	8	sn	sn	PROPN
ejpam-1854	123	9	�	�	PROPN
ejpam-1854	123	10	�	�	PROPN
ejpam-1854	123	11	1	1	NUM
ejpam-1854	123	12	n	n	PROPN
ejpam-1854	123	13	=	=	SYM
ejpam-1854	123	14	�	�	PROPN
ejpam-1854	123	15	�	�	PROPN
ejpam-1854	123	16	�	�	PROPN
ejpam-1854	123	17	�	�	PROPN
ejpam-1854	123	18	�	�	PROPN
ejpam-1854	123	19	∞	∞	PROPN
ejpam-1854	123	20	∑	∑	PROPN
ejpam-1854	123	21	i=1	i=1	PROPN
ejpam-1854	123	22	zn+i	zn+i	PROPN
ejpam-1854	123	23	�	�	PROPN
ejpam-1854	123	24	�	�	PROPN
ejpam-1854	123	25	�	�	PROPN
ejpam-1854	123	26	�	�	PROPN
ejpam-1854	123	27	�	�	PROPN
ejpam-1854	123	28	1	1	NUM
ejpam-1854	123	29	n	n	PROPN
ejpam-1854	123	30	=	=	SYM
ejpam-1854	123	31	�	�	PROPN
ejpam-1854	123	32	max	max	PROPN
ejpam-1854	123	33	¦	¦	PROPN
ejpam-1854	123	34	�	�	PROPN
ejpam-1854	123	35	�	�	PROPN
ejpam-1854	123	36	zn+1	zn+1	PROPN
ejpam-1854	123	37	�	�	PROPN
ejpam-1854	123	38	�	�	PROPN
ejpam-1854	123	39	,	,	PUNCT
ejpam-1854	123	40	�	�	PROPN
ejpam-1854	123	41	�	�	PROPN
ejpam-1854	123	42	an+2	an+2	PROPN
ejpam-1854	123	43	�	�	PROPN
ejpam-1854	123	44	�	�	PROPN
ejpam-1854	123	45	,	,	PUNCT
ejpam-1854	123	46	.	.	PUNCT
ejpam-1854	123	47	.	.	PUNCT
ejpam-1854	123	48	.	.	PUNCT
ejpam-1854	124	1	©	©	PROPN
ejpam-1854	124	2	�	�	PROPN
ejpam-1854	124	3	1	1	NUM
ejpam-1854	124	4	n	n	PROPN
ejpam-1854	124	5	where	where	SCONJ
ejpam-1854	124	6	sn	sn	ADV
ejpam-1854	124	7	=	=	PUNCT
ejpam-1854	125	1	∑n	∑n	NOUN
ejpam-1854	125	2	i=1	i=1	PROPN
ejpam-1854	125	3	ai	ai	VERB
ejpam-1854	125	4	.	.	PUNCT
ejpam-1854	126	1	hence	hence	ADV
ejpam-1854	126	2	,	,	PUNCT
ejpam-1854	126	3	from	from	ADP
ejpam-1854	126	4	the	the	DET
ejpam-1854	126	5	condition	condition	NOUN
ejpam-1854	126	6	(	(	PUNCT
ejpam-1854	126	7	5	5	X
ejpam-1854	126	8	)	)	PUNCT
ejpam-1854	126	9	we	we	PRON
ejpam-1854	126	10	obtain	obtain	VERB
ejpam-1854	126	11	0	0	NUM
ejpam-1854	126	12	<	<	X
ejpam-1854	126	13	�	�	PROPN
ejpam-1854	126	14	�	�	PROPN
ejpam-1854	126	15	α−	α−	ADP
ejpam-1854	126	16	sn	sn	PROPN
ejpam-1854	126	17	�	�	PROPN
ejpam-1854	126	18	�	�	PROPN
ejpam-1854	126	19	1	1	NUM
ejpam-1854	126	20	n	n	PROPN
ejpam-1854	126	21	=	=	PROPN
ejpam-1854	126	22	�	�	PROPN
ejpam-1854	126	23	�	�	PROPN
ejpam-1854	126	24	zn+1	zn+1	PROPN
ejpam-1854	126	25	�	�	PROPN
ejpam-1854	126	26	�	�	PROPN
ejpam-1854	126	27	1	1	NUM
ejpam-1854	126	28	n	n	NOUN
ejpam-1854	126	29	.	.	PUNCT
ejpam-1854	127	1	thus	thus	ADV
ejpam-1854	127	2	,	,	PUNCT
ejpam-1854	127	3	0	0	X
ejpam-1854	127	4	<	<	X
ejpam-1854	127	5	�	�	PROPN
ejpam-1854	127	6	�	�	PROPN
ejpam-1854	127	7	α−	α−	ADP
ejpam-1854	127	8	sn	sn	PROPN
ejpam-1854	127	9	�	�	PROPN
ejpam-1854	127	10	�	�	PROPN
ejpam-1854	127	11	1	1	NUM
ejpam-1854	127	12	n	n	PROPN
ejpam-1854	127	13	=	=	NOUN
ejpam-1854	127	14	h	h	NOUN
ejpam-1854	127	15	edeg(zn+1	edeg(zn+1	PROPN
ejpam-1854	127	16	)	)	PUNCT
ejpam-1854	128	1	i	i	PRON
ejpam-1854	128	2	1	1	NUM
ejpam-1854	128	3	n	n	CCONJ
ejpam-1854	128	4	and	and	CCONJ
ejpam-1854	128	5	by	by	ADP
ejpam-1854	128	6	the	the	DET
ejpam-1854	128	7	inequality	inequality	NOUN
ejpam-1854	128	8	(	(	PUNCT
ejpam-1854	128	9	6	6	NUM
ejpam-1854	128	10	)	)	PUNCT
ejpam-1854	128	11	we	we	PRON
ejpam-1854	128	12	get	get	VERB
ejpam-1854	128	13	0	0	NUM
ejpam-1854	128	14	<	<	X
ejpam-1854	128	15	�	�	PROPN
ejpam-1854	128	16	�	�	PROPN
ejpam-1854	128	17	α−	α−	ADP
ejpam-1854	128	18	sn	sn	PROPN
ejpam-1854	128	19	�	�	PROPN
ejpam-1854	128	20	�	�	PROPN
ejpam-1854	128	21	1	1	NUM
ejpam-1854	128	22	n	n	PROPN
ejpam-1854	128	23	=	=	NOUN
ejpam-1854	128	24	h	h	NOUN
ejpam-1854	128	25	edeg(zn+1	edeg(zn+1	PROPN
ejpam-1854	128	26	)	)	PUNCT
ejpam-1854	129	1	i	i	PRON
ejpam-1854	129	2	1	1	NUM
ejpam-1854	129	3	n	n	ADV
ejpam-1854	129	4	≤	≤	NOUN
ejpam-1854	129	5	e−	e−	PROPN
ejpam-1854	129	6	n1+ε	n1+ε	PROPN
ejpam-1854	129	7	n	n	NOUN
ejpam-1854	129	8	=	=	NOUN
ejpam-1854	129	9	e−nε	e−nε	NOUN
ejpam-1854	129	10	for	for	ADP
ejpam-1854	129	11	n	n	CCONJ
ejpam-1854	129	12	>	>	X
ejpam-1854	129	13	n0	n0	X
ejpam-1854	129	14	(	(	PUNCT
ejpam-1854	129	15	ε	ε	PROPN
ejpam-1854	129	16	)	)	PUNCT
ejpam-1854	129	17	.	.	PUNCT
ejpam-1854	130	1	thus	thus	ADV
ejpam-1854	130	2	,	,	PUNCT
ejpam-1854	130	3	we	we	PRON
ejpam-1854	130	4	have	have	VERB
ejpam-1854	130	5	�	�	PROPN
ejpam-1854	130	6	�	�	PROPN
ejpam-1854	130	7	α−	α−	ADP
ejpam-1854	130	8	sn	sn	PROPN
ejpam-1854	130	9	�	�	PROPN
ejpam-1854	130	10	�	�	PROPN
ejpam-1854	130	11	1	1	NUM
ejpam-1854	130	12	n	n	PROPN
ejpam-1854	130	13	→	→	X
ejpam-1854	130	14	0(n→∞	0(n→∞	NUM
ejpam-1854	130	15	)	)	PUNCT
ejpam-1854	130	16	.	.	PUNCT
ejpam-1854	131	1	since	since	SCONJ
ejpam-1854	131	2	sn	sn	PROPN
ejpam-1854	131	3	∈	∈	PROPN
ejpam-1854	131	4	k	k	PROPN
ejpam-1854	131	5	〈	〈	PROPN
ejpam-1854	131	6	x	x	X
ejpam-1854	131	7	〉	〉	NOUN
ejpam-1854	131	8	for	for	ADP
ejpam-1854	131	9	every	every	DET
ejpam-1854	131	10	n	n	PRON
ejpam-1854	131	11	∈	∈	PROPN
ejpam-1854	131	12	n	n	CCONJ
ejpam-1854	131	13	,	,	PUNCT
ejpam-1854	131	14	and	and	CCONJ
ejpam-1854	131	15	the	the	DET
ejpam-1854	131	16	rational	rational	ADJ
ejpam-1854	131	17	polynomials	polynomial	NOUN
ejpam-1854	131	18	field	field	NOUN
ejpam-1854	131	19	set	set	VERB
ejpam-1854	131	20	k(x	k(x	PROPN
ejpam-1854	131	21	)	)	PUNCT
ejpam-1854	131	22	is	be	AUX
ejpam-1854	131	23	dense	dense	ADJ
ejpam-1854	131	24	in	in	ADP
ejpam-1854	131	25	k	k	PROPN
ejpam-1854	131	26	〈	〈	PROPN
ejpam-1854	131	27	x	x	X
ejpam-1854	131	28	〉	〉	NOUN
ejpam-1854	131	29	with	with	ADP
ejpam-1854	131	30	respect	respect	NOUN
ejpam-1854	131	31	the	the	DET
ejpam-1854	131	32	non	non	ADJ
ejpam-1854	131	33	-	-	ADJ
ejpam-1854	131	34	archimedean	archimedean	ADJ
ejpam-1854	131	35	norm	norm	NOUN
ejpam-1854	131	36	,	,	PUNCT
ejpam-1854	131	37	there	there	PRON
ejpam-1854	131	38	exists	exist	VERB
ejpam-1854	131	39	a	a	DET
ejpam-1854	131	40	sequence	sequence	NOUN
ejpam-1854	131	41	an	an	DET
ejpam-1854	131	42	bn	bn	NOUN
ejpam-1854	131	43	∈	∈	PROPN
ejpam-1854	131	44	k(x	k(x	PROPN
ejpam-1854	131	45	)	)	PUNCT
ejpam-1854	131	46	(	(	PUNCT
ejpam-1854	131	47	an	an	X
ejpam-1854	131	48	,	,	PUNCT
ejpam-1854	131	49	bn	bn	NOUN
ejpam-1854	131	50	∈	∈	PROPN
ejpam-1854	131	51	k[x	k[x	PROPN
ejpam-1854	131	52	]	]	PUNCT
ejpam-1854	131	53	)	)	PUNCT
ejpam-1854	131	54	such	such	ADJ
ejpam-1854	131	55	that	that	SCONJ
ejpam-1854	131	56	�	�	PROPN
ejpam-1854	131	57	�	�	PROPN
ejpam-1854	131	58	�	�	PROPN
ejpam-1854	131	59	�	�	PROPN
ejpam-1854	131	60	sn−	sn−	PROPN
ejpam-1854	131	61	an	an	DET
ejpam-1854	131	62	bn	bn	PROPN
ejpam-1854	131	63	�	�	PROPN
ejpam-1854	131	64	�	�	PROPN
ejpam-1854	131	65	�	�	PROPN
ejpam-1854	131	66	�	�	PROPN
ejpam-1854	131	67	<	<	X
ejpam-1854	131	68	�	�	PROPN
ejpam-1854	131	69	�	�	PROPN
ejpam-1854	131	70	α−	α−	ADP
ejpam-1854	131	71	sn	sn	PROPN
ejpam-1854	131	72	�	�	PROPN
ejpam-1854	131	73	�	�	PROPN
ejpam-1854	131	74	references	reference	NOUN
ejpam-1854	131	75	245	245	NUM
ejpam-1854	131	76	for	for	ADP
ejpam-1854	131	77	every	every	DET
ejpam-1854	131	78	n	n	CCONJ
ejpam-1854	131	79	∈	∈	NOUN
ejpam-1854	131	80	n.	n.	NOUN
ejpam-1854	131	81	by	by	ADP
ejpam-1854	131	82	the	the	DET
ejpam-1854	131	83	ultrametric	ultrametric	ADJ
ejpam-1854	131	84	inequality	inequality	NOUN
ejpam-1854	131	85	we	we	PRON
ejpam-1854	131	86	can	can	AUX
ejpam-1854	131	87	write	write	VERB
ejpam-1854	131	88	�	�	PROPN
ejpam-1854	131	89	�	�	PROPN
ejpam-1854	131	90	�	�	PROPN
ejpam-1854	131	91	�	�	PROPN
ejpam-1854	131	92	α−	α−	ADP
ejpam-1854	131	93	an	an	DET
ejpam-1854	131	94	bn	bn	PROPN
ejpam-1854	131	95	�	�	PROPN
ejpam-1854	131	96	�	�	PROPN
ejpam-1854	131	97	�	�	PROPN
ejpam-1854	131	98	�	�	PROPN
ejpam-1854	131	99	≤max	≤max	NUM
ejpam-1854	131	100	¦	¦	PROPN
ejpam-1854	131	101	�	�	PROPN
ejpam-1854	131	102	�	�	PROPN
ejpam-1854	131	103	α−	α−	ADP
ejpam-1854	131	104	sn	sn	PROPN
ejpam-1854	131	105	�	�	PROPN
ejpam-1854	131	106	�	�	PROPN
ejpam-1854	131	107	,	,	PUNCT
ejpam-1854	131	108	�	�	PROPN
ejpam-1854	131	109	�	�	PROPN
ejpam-1854	131	110	sn−	sn−	PROPN
ejpam-1854	131	111	bn	bn	PROPN
ejpam-1854	131	112	�	�	PROPN
ejpam-1854	131	113	�	�	PROPN
ejpam-1854	131	114	©	©	PROPN
ejpam-1854	131	115	=	=	PROPN
ejpam-1854	131	116	�	�	PROPN
ejpam-1854	131	117	�	�	PROPN
ejpam-1854	131	118	α−	α−	ADP
ejpam-1854	131	119	sn	sn	PROPN
ejpam-1854	131	120	�	�	PROPN
ejpam-1854	131	121	�	�	PROPN
ejpam-1854	131	122	for	for	ADP
ejpam-1854	131	123	every	every	DET
ejpam-1854	131	124	n	n	CCONJ
ejpam-1854	131	125	∈	∈	PROPN
ejpam-1854	131	126	n.	n.	NOUN
ejpam-1854	131	127	hence	hence	ADV
ejpam-1854	131	128	,	,	PUNCT
ejpam-1854	131	129	we	we	PRON
ejpam-1854	131	130	can	can	AUX
ejpam-1854	131	131	obtain	obtain	VERB
ejpam-1854	131	132	an	an	DET
ejpam-1854	131	133	bn	bn	NOUN
ejpam-1854	131	134	∈	∈	PROPN
ejpam-1854	131	135	k(x	k(x	PROPN
ejpam-1854	131	136	)	)	PUNCT
ejpam-1854	131	137	such	such	ADJ
ejpam-1854	131	138	that	that	SCONJ
ejpam-1854	131	139	�	�	PROPN
ejpam-1854	131	140	�	�	PROPN
ejpam-1854	131	141	�	�	PROPN
ejpam-1854	131	142	�	�	PROPN
ejpam-1854	131	143	α−	α−	ADP
ejpam-1854	131	144	an	an	DET
ejpam-1854	131	145	bn	bn	PROPN
ejpam-1854	131	146	�	�	PROPN
ejpam-1854	131	147	�	�	PROPN
ejpam-1854	131	148	�	�	PROPN
ejpam-1854	131	149	�	�	PROPN
ejpam-1854	131	150	1	1	NUM
ejpam-1854	131	151	n	n	PROPN
ejpam-1854	131	152	≤	≤	NUM
ejpam-1854	131	153	�	�	PROPN
ejpam-1854	131	154	�	�	PROPN
ejpam-1854	131	155	α−	α−	ADP
ejpam-1854	131	156	sn	sn	PROPN
ejpam-1854	131	157	�	�	PROPN
ejpam-1854	131	158	�	�	PROPN
ejpam-1854	131	159	1	1	NUM
ejpam-1854	131	160	n	n	PROPN
ejpam-1854	131	161	=	=	NOUN
ejpam-1854	131	162	e−nε	e−nε	NOUN
ejpam-1854	131	163	→	→	SYM
ejpam-1854	131	164	0	0	NUM
ejpam-1854	131	165	(	(	PUNCT
ejpam-1854	131	166	n→∞	n→∞	NUM
ejpam-1854	131	167	)	)	PUNCT
ejpam-1854	131	168	.	.	PUNCT
ejpam-1854	132	1	so	so	ADV
ejpam-1854	132	2	,	,	PUNCT
ejpam-1854	132	3	α	α	PROPN
ejpam-1854	132	4	∈	∈	PROPN
ejpam-1854	132	5	k	k	X
ejpam-1854	132	6	〈	〈	PROPN
ejpam-1854	132	7	x	x	NOUN
ejpam-1854	132	8	〉	〉	NOUN
ejpam-1854	132	9	is	be	AUX
ejpam-1854	132	10	a	a	DET
ejpam-1854	132	11	liouville	liouville	NOUN
ejpam-1854	132	12	number	number	NOUN
ejpam-1854	132	13	.	.	PUNCT
ejpam-1854	132	14	example	example	NOUN
ejpam-1854	133	1	2	2	NUM
ejpam-1854	133	2	.	.	X
ejpam-1854	133	3	consider	consider	VERB
ejpam-1854	133	4	the	the	DET
ejpam-1854	133	5	element	element	NOUN
ejpam-1854	133	6	ξ	ξ	X
ejpam-1854	133	7	=	=	PUNCT
ejpam-1854	133	8	∑∞	∑∞	NOUN
ejpam-1854	133	9	n=1	n=1	PROPN
ejpam-1854	133	10	x−n	x−n	PROPN
ejpam-1854	133	11	!	!	PUNCT
ejpam-1854	134	1	in	in	ADP
ejpam-1854	134	2	k	k	PROPN
ejpam-1854	134	3	〈	〈	PROPN
ejpam-1854	134	4	x	x	X
ejpam-1854	134	5	〉	〉	NOUN
ejpam-1854	134	6	.	.	PUNCT
ejpam-1854	135	1	let	let	VERB
ejpam-1854	135	2	zn	zn	NOUN
ejpam-1854	135	3	=	=	SYM
ejpam-1854	135	4	x−n	x−n	PROPN
ejpam-1854	135	5	!	!	PUNCT
ejpam-1854	135	6	.	.	PUNCT
ejpam-1854	136	1	it	it	PRON
ejpam-1854	136	2	is	be	AUX
ejpam-1854	136	3	clear	clear	ADJ
ejpam-1854	136	4	that	that	SCONJ
ejpam-1854	136	5	zn	zn	PROPN
ejpam-1854	136	6	satisfy	satisfy	VERB
ejpam-1854	136	7	the	the	DET
ejpam-1854	136	8	conditions	condition	NOUN
ejpam-1854	136	9	(	(	PUNCT
ejpam-1854	136	10	5	5	NUM
ejpam-1854	136	11	)	)	PUNCT
ejpam-1854	136	12	and	and	CCONJ
ejpam-1854	136	13	(	(	PUNCT
ejpam-1854	136	14	6	6	NUM
ejpam-1854	136	15	)	)	PUNCT
ejpam-1854	136	16	.	.	PUNCT
ejpam-1854	137	1	by	by	ADP
ejpam-1854	137	2	theorem	theorem	NOUN
ejpam-1854	137	3	3	3	NUM
ejpam-1854	137	4	,	,	PUNCT
ejpam-1854	137	5	ξ	ξ	PROPN
ejpam-1854	137	6	is	be	AUX
ejpam-1854	137	7	a	a	DET
ejpam-1854	137	8	liouville	liouville	NOUN
ejpam-1854	137	9	number	number	NOUN
ejpam-1854	137	10	in	in	ADP
ejpam-1854	137	11	the	the	DET
ejpam-1854	137	12	functions	function	NOUN
ejpam-1854	137	13	field	field	NOUN
ejpam-1854	137	14	.	.	PUNCT
ejpam-1854	138	1	acknowledgements	acknowledgement	NOUN
ejpam-1854	138	2	this	this	DET
ejpam-1854	138	3	work	work	NOUN
ejpam-1854	138	4	is	be	AUX
ejpam-1854	138	5	supported	support	VERB
ejpam-1854	138	6	by	by	ADP
ejpam-1854	138	7	mersin	mersin	PROPN
ejpam-1854	138	8	university	university	PROPN
ejpam-1854	138	9	and	and	CCONJ
ejpam-1854	138	10	the	the	DET
ejpam-1854	138	11	scientific	scientific	ADJ
ejpam-1854	138	12	and	and	CCONJ
ejpam-1854	138	13	technological	technological	ADJ
ejpam-1854	138	14	research	research	NOUN
ejpam-1854	138	15	council	council	NOUN
ejpam-1854	138	16	of	of	ADP
ejpam-1854	138	17	turkey	turkey	PROPN
ejpam-1854	138	18	(	(	PUNCT
ejpam-1854	138	19	tübi̇tak	tübi̇tak	NUM
ejpam-1854	138	20	)	)	PUNCT
ejpam-1854	138	21	.	.	PUNCT
ejpam-1854	139	1	the	the	DET
ejpam-1854	139	2	authors	author	NOUN
ejpam-1854	139	3	would	would	AUX
ejpam-1854	139	4	like	like	VERB
ejpam-1854	139	5	to	to	PART
ejpam-1854	139	6	thank	thank	VERB
ejpam-1854	139	7	the	the	DET
ejpam-1854	139	8	reviewers	reviewer	NOUN
ejpam-1854	139	9	for	for	ADP
ejpam-1854	139	10	their	their	PRON
ejpam-1854	139	11	useful	useful	ADJ
ejpam-1854	139	12	suggestions	suggestion	NOUN
ejpam-1854	139	13	.	.	PUNCT
ejpam-1854	140	1	references	reference	NOUN
ejpam-1854	140	2	[	[	X
ejpam-1854	140	3	1	1	NUM
ejpam-1854	140	4	]	]	X
ejpam-1854	140	5	w.w	w.w	PROPN
ejpam-1854	140	6	.	.	PROPN
ejpam-1854	140	7	adams	adams	PROPN
ejpam-1854	140	8	.	.	PUNCT
ejpam-1854	141	1	transcendental	transcendental	ADJ
ejpam-1854	141	2	numbers	number	NOUN
ejpam-1854	141	3	in	in	ADP
ejpam-1854	141	4	the	the	DET
ejpam-1854	141	5	p	p	NOUN
ejpam-1854	141	6	-	-	PUNCT
ejpam-1854	141	7	adic	adic	ADJ
ejpam-1854	141	8	domain	domain	NOUN
ejpam-1854	141	9	,	,	PUNCT
ejpam-1854	141	10	american	american	ADJ
ejpam-1854	141	11	journal	journal	NOUN
ejpam-1854	141	12	of	of	ADP
ejpam-1854	141	13	mathematics	mathematic	NOUN
ejpam-1854	141	14	.	.	PUNCT
ejpam-1854	142	1	88	88	NUM
ejpam-1854	142	2	,	,	PUNCT
ejpam-1854	142	3	279	279	NUM
ejpam-1854	142	4	-	-	SYM
ejpam-1854	142	5	308	308	NUM
ejpam-1854	142	6	.	.	PUNCT
ejpam-1854	143	1	1966	1966	NUM
ejpam-1854	143	2	.	.	PUNCT
ejpam-1854	144	1	[	[	X
ejpam-1854	144	2	2	2	NUM
ejpam-1854	144	3	]	]	PUNCT
ejpam-1854	144	4	k.	k.	NOUN
ejpam-1854	144	5	alniaçik	alniaçik	PROPN
ejpam-1854	144	6	.	.	PUNCT
ejpam-1854	145	1	on	on	ADP
ejpam-1854	145	2	um	um	INTJ
ejpam-1854	145	3	-	-	PUNCT
ejpam-1854	145	4	numbers	number	NOUN
ejpam-1854	145	5	,	,	PUNCT
ejpam-1854	145	6	proceedings	proceeding	NOUN
ejpam-1854	145	7	of	of	ADP
ejpam-1854	145	8	the	the	DET
ejpam-1854	145	9	american	american	PROPN
ejpam-1854	145	10	mathematical	mathematical	PROPN
ejpam-1854	145	11	society	society	NOUN
ejpam-1854	145	12	.	.	PUNCT
ejpam-1854	145	13	85	85	NUM
ejpam-1854	145	14	,	,	PUNCT
ejpam-1854	145	15	no	no	INTJ
ejpam-1854	145	16	.	.	NOUN
ejpam-1854	145	17	4	4	NUM
ejpam-1854	145	18	,	,	PUNCT
ejpam-1854	145	19	499	499	NUM
ejpam-1854	145	20	-	-	SYM
ejpam-1854	145	21	505	505	NUM
ejpam-1854	145	22	.	.	PUNCT
ejpam-1854	145	23	1982	1982	NUM
ejpam-1854	145	24	.	.	PUNCT
ejpam-1854	146	1	[	[	X
ejpam-1854	146	2	3	3	NUM
ejpam-1854	146	3	]	]	PUNCT
ejpam-1854	146	4	a.	a.	NOUN
ejpam-1854	146	5	baker	baker	PROPN
ejpam-1854	146	6	.	.	PUNCT
ejpam-1854	147	1	transcendental	transcendental	ADJ
ejpam-1854	147	2	number	number	NOUN
ejpam-1854	147	3	theory	theory	NOUN
ejpam-1854	147	4	,	,	PUNCT
ejpam-1854	147	5	cambridge	cambridge	PROPN
ejpam-1854	147	6	university	university	PROPN
ejpam-1854	147	7	press	press	PROPN
ejpam-1854	147	8	,	,	PUNCT
ejpam-1854	147	9	cambridge	cambridge	PROPN
ejpam-1854	147	10	,	,	PUNCT
ejpam-1854	147	11	1975	1975	NUM
ejpam-1854	147	12	.	.	PUNCT
ejpam-1854	148	1	[	[	X
ejpam-1854	148	2	4	4	NUM
ejpam-1854	148	3	]	]	X
ejpam-1854	148	4	v.v	v.v	PROPN
ejpam-1854	148	5	.	.	PROPN
ejpam-1854	148	6	beresnevich	beresnevich	PROPN
ejpam-1854	148	7	,	,	PUNCT
ejpam-1854	148	8	v.i	v.i	PROPN
ejpam-1854	148	9	.	.	PROPN
ejpam-1854	148	10	bernik	bernik	PROPN
ejpam-1854	148	11	,	,	PUNCT
ejpam-1854	148	12	and	and	CCONJ
ejpam-1854	148	13	e.i	e.i	PROPN
ejpam-1854	148	14	.	.	PROPN
ejpam-1854	148	15	kovalevskaya	kovalevskaya	PROPN
ejpam-1854	148	16	.	.	PUNCT
ejpam-1854	149	1	on	on	ADP
ejpam-1854	149	2	approximation	approximation	NOUN
ejpam-1854	149	3	of	of	ADP
ejpam-1854	149	4	p	p	NOUN
ejpam-1854	149	5	-	-	PUNCT
ejpam-1854	149	6	adic	adic	ADJ
ejpam-1854	149	7	numbers	number	NOUN
ejpam-1854	149	8	by	by	ADP
ejpam-1854	149	9	p	p	NOUN
ejpam-1854	149	10	-	-	PUNCT
ejpam-1854	149	11	adic	adic	ADJ
ejpam-1854	149	12	algebraic	algebraic	ADJ
ejpam-1854	149	13	numbers	number	NOUN
ejpam-1854	149	14	,	,	PUNCT
ejpam-1854	149	15	journal	journal	NOUN
ejpam-1854	149	16	of	of	ADP
ejpam-1854	149	17	number	number	NOUN
ejpam-1854	149	18	theory	theory	NOUN
ejpam-1854	149	19	.	.	PUNCT
ejpam-1854	150	1	111	111	NUM
ejpam-1854	150	2	33	33	NUM
ejpam-1854	150	3	56	56	NUM
ejpam-1854	150	4	.	.	PUNCT
ejpam-1854	150	5	2005	2005	NUM
ejpam-1854	150	6	.	.	PUNCT
ejpam-1854	151	1	[	[	X
ejpam-1854	151	2	5	5	X
ejpam-1854	151	3	]	]	X
ejpam-1854	151	4	y.	y.	PROPN
ejpam-1854	151	5	bugeaud	bugeaud	PROPN
ejpam-1854	151	6	.	.	PUNCT
ejpam-1854	152	1	approximation	approximation	NOUN
ejpam-1854	152	2	by	by	ADP
ejpam-1854	152	3	algebraic	algebraic	ADJ
ejpam-1854	152	4	numbers	number	NOUN
ejpam-1854	152	5	,	,	PUNCT
ejpam-1854	152	6	cambridge	cambridge	PROPN
ejpam-1854	152	7	university	university	PROPN
ejpam-1854	152	8	press	press	PROPN
ejpam-1854	152	9	,	,	PUNCT
ejpam-1854	152	10	cambridge	cambridge	PROPN
ejpam-1854	152	11	.	.	PROPN
ejpam-1854	152	12	2007	2007	NUM
ejpam-1854	152	13	.	.	PUNCT
ejpam-1854	153	1	[	[	X
ejpam-1854	153	2	6	6	NUM
ejpam-1854	153	3	]	]	SYM
ejpam-1854	153	4	d.n	d.n	PROPN
ejpam-1854	153	5	.	.	PROPN
ejpam-1854	153	6	clark	clark	PROPN
ejpam-1854	153	7	.	.	PUNCT
ejpam-1854	154	1	a	a	DET
ejpam-1854	154	2	note	note	NOUN
ejpam-1854	154	3	on	on	ADP
ejpam-1854	154	4	the	the	DET
ejpam-1854	154	5	p	p	NOUN
ejpam-1854	154	6	-	-	PUNCT
ejpam-1854	154	7	adic	adic	ADJ
ejpam-1854	154	8	convergence	convergence	NOUN
ejpam-1854	154	9	of	of	ADP
ejpam-1854	154	10	the	the	DET
ejpam-1854	154	11	solutions	solution	NOUN
ejpam-1854	154	12	of	of	ADP
ejpam-1854	154	13	linear	linear	PROPN
ejpam-1854	154	14	differential	differential	ADJ
ejpam-1854	154	15	equations	equation	NOUN
ejpam-1854	154	16	,	,	PUNCT
ejpam-1854	154	17	proceedings	proceeding	NOUN
ejpam-1854	154	18	of	of	ADP
ejpam-1854	154	19	the	the	DET
ejpam-1854	154	20	american	american	PROPN
ejpam-1854	154	21	mathematical	mathematical	PROPN
ejpam-1854	154	22	society	society	NOUN
ejpam-1854	154	23	.	.	PUNCT
ejpam-1854	155	1	17	17	NUM
ejpam-1854	155	2	,	,	PUNCT
ejpam-1854	155	3	262	262	NUM
ejpam-1854	155	4	-	-	SYM
ejpam-1854	155	5	269	269	NUM
ejpam-1854	155	6	.	.	NUM
ejpam-1854	155	7	1966	1966	NUM
ejpam-1854	155	8	.	.	PUNCT
ejpam-1854	156	1	[	[	X
ejpam-1854	156	2	7	7	X
ejpam-1854	156	3	]	]	PUNCT
ejpam-1854	156	4	p.	p.	PROPN
ejpam-1854	156	5	erdös	erdös	PROPN
ejpam-1854	156	6	.	.	PUNCT
ejpam-1854	157	1	representation	representation	NOUN
ejpam-1854	157	2	of	of	ADP
ejpam-1854	157	3	real	real	ADJ
ejpam-1854	157	4	numbers	number	NOUN
ejpam-1854	157	5	as	as	ADP
ejpam-1854	157	6	sums	sum	NOUN
ejpam-1854	157	7	and	and	CCONJ
ejpam-1854	157	8	products	product	NOUN
ejpam-1854	157	9	of	of	ADP
ejpam-1854	157	10	liouville	liouville	NOUN
ejpam-1854	157	11	numbers	number	NOUN
ejpam-1854	157	12	,	,	PUNCT
ejpam-1854	157	13	michigan	michigan	PROPN
ejpam-1854	157	14	mathematical	mathematical	PROPN
ejpam-1854	157	15	journal	journal	PROPN
ejpam-1854	157	16	.	.	PUNCT
ejpam-1854	158	1	9	9	NUM
ejpam-1854	158	2	,	,	PUNCT
ejpam-1854	158	3	59	59	NUM
ejpam-1854	158	4	-	-	SYM
ejpam-1854	158	5	60	60	NUM
ejpam-1854	158	6	.	.	PUNCT
ejpam-1854	159	1	1962	1962	NUM
ejpam-1854	159	2	.	.	PUNCT
ejpam-1854	160	1	[	[	X
ejpam-1854	160	2	8	8	X
ejpam-1854	160	3	]	]	PUNCT
ejpam-1854	160	4	p.	p.	NOUN
ejpam-1854	160	5	erdös	erdös	PROPN
ejpam-1854	160	6	.	.	PUNCT
ejpam-1854	161	1	some	some	DET
ejpam-1854	161	2	problems	problem	NOUN
ejpam-1854	161	3	and	and	CCONJ
ejpam-1854	161	4	results	result	NOUN
ejpam-1854	161	5	on	on	ADP
ejpam-1854	161	6	the	the	DET
ejpam-1854	161	7	irrationality	irrationality	NOUN
ejpam-1854	161	8	of	of	ADP
ejpam-1854	161	9	the	the	DET
ejpam-1854	161	10	sum	sum	NOUN
ejpam-1854	161	11	of	of	ADP
ejpam-1854	161	12	infinite	infinite	ADJ
ejpam-1854	161	13	series	series	NOUN
ejpam-1854	161	14	,	,	PUNCT
ejpam-1854	161	15	journal	journal	NOUN
ejpam-1854	161	16	of	of	ADP
ejpam-1854	161	17	mathematical	mathematical	ADJ
ejpam-1854	161	18	sciences	science	NOUN
ejpam-1854	161	19	.	.	PUNCT
ejpam-1854	162	1	10	10	NUM
ejpam-1854	162	2	,	,	PUNCT
ejpam-1854	162	3	1	1	NUM
ejpam-1854	162	4	-	-	SYM
ejpam-1854	162	5	7	7	NUM
ejpam-1854	162	6	.	.	NUM
ejpam-1854	162	7	1975	1975	NUM
ejpam-1854	162	8	.	.	PUNCT
ejpam-1854	163	1	[	[	X
ejpam-1854	163	2	9	9	X
ejpam-1854	163	3	]	]	PUNCT
ejpam-1854	163	4	j.	j.	PROPN
ejpam-1854	163	5	hancl	hancl	PROPN
ejpam-1854	163	6	.	.	PUNCT
ejpam-1854	164	1	liouville	liouville	PROPN
ejpam-1854	164	2	sequences	sequence	NOUN
ejpam-1854	164	3	,	,	PUNCT
ejpam-1854	164	4	nagoya	nagoya	PROPN
ejpam-1854	164	5	mathematical	mathematical	PROPN
ejpam-1854	164	6	journal	journal	PROPN
ejpam-1854	164	7	.	.	PUNCT
ejpam-1854	165	1	j.	j.	PROPN
ejpam-1854	165	2	172	172	NUM
ejpam-1854	165	3	,	,	PUNCT
ejpam-1854	165	4	173	173	NUM
ejpam-1854	165	5	-	-	SYM
ejpam-1854	165	6	187	187	NUM
ejpam-1854	165	7	.	.	NUM
ejpam-1854	165	8	2003	2003	NUM
ejpam-1854	165	9	.	.	PUNCT
ejpam-1854	166	1	references	reference	NOUN
ejpam-1854	166	2	246	246	NUM
ejpam-1854	167	1	[	[	X
ejpam-1854	167	2	10	10	NUM
ejpam-1854	167	3	]	]	X
ejpam-1854	167	4	j.f	j.f	PROPN
ejpam-1854	167	5	.	.	PROPN
ejpam-1854	167	6	koksma	koksma	PROPN
ejpam-1854	167	7	.	.	PUNCT
ejpam-1854	168	1	uber	uber	PROPN
ejpam-1854	168	2	die	die	VERB
ejpam-1854	168	3	mahlersche	mahlersche	PROPN
ejpam-1854	168	4	kiasseneinteilung	kiasseneinteilung	PROPN
ejpam-1854	168	5	der	der	PROPN
ejpam-1854	168	6	transzendenten	transzendenten	VERB
ejpam-1854	168	7	zahlen	zahlen	NUM
ejpam-1854	168	8	und	und	NOUN
ejpam-1854	168	9	die	die	PROPN
ejpam-1854	168	10	approximation	approximation	PROPN
ejpam-1854	168	11	komplexer	komplexer	PROPN
ejpam-1854	168	12	durch	durch	PROPN
ejpam-1854	168	13	algebraische	algebraische	PROPN
ejpam-1854	168	14	zahlen	zahlen	PROPN
ejpam-1854	168	15	.	.	PUNCT
ejpam-1854	169	1	monatshefte	monatshefte	PROPN
ejpam-1854	169	2	für	für	PROPN
ejpam-1854	169	3	mathematik	mathematik	PROPN
ejpam-1854	169	4	und	und	PROPN
ejpam-1854	169	5	physik	physik	PROPN
ejpam-1854	169	6	.	.	PROPN
ejpam-1854	170	1	48	48	NUM
ejpam-1854	170	2	,	,	PUNCT
ejpam-1854	170	3	176i	176i	PROPN
ejpam-1854	170	4	89	89	NUM
ejpam-1854	170	5	.	.	PUNCT
ejpam-1854	170	6	1939	1939	NUM
ejpam-1854	170	7	.	.	PUNCT
ejpam-1854	171	1	[	[	X
ejpam-1854	171	2	11	11	NUM
ejpam-1854	171	3	]	]	PUNCT
ejpam-1854	171	4	t.	t.	PROPN
ejpam-1854	171	5	chaichana	chaichana	PROPN
ejpam-1854	171	6	,	,	PUNCT
ejpam-1854	171	7	t.	t.	PROPN
ejpam-1854	171	8	komatsu	komatsu	PROPN
ejpam-1854	171	9	,	,	PUNCT
ejpam-1854	171	10	and	and	CCONJ
ejpam-1854	171	11	v.	v.	ADP
ejpam-1854	171	12	laohakosol	laohakosol	NOUN
ejpam-1854	171	13	.	.	PUNCT
ejpam-1854	172	1	liouville	liouville	NOUN
ejpam-1854	172	2	numbers	number	NOUN
ejpam-1854	172	3	in	in	ADP
ejpam-1854	172	4	the	the	DET
ejpam-1854	172	5	non	non	ADJ
ejpam-1854	172	6	-	-	ADJ
ejpam-1854	172	7	archimedean	archimedean	ADJ
ejpam-1854	172	8	case	case	NOUN
ejpam-1854	172	9	,	,	PUNCT
ejpam-1854	172	10	publicationes	publicatione	NOUN
ejpam-1854	172	11	mathematicae	mathematicae	PROPN
ejpam-1854	172	12	debrecen	debrecen	PROPN
ejpam-1854	172	13	.	.	PUNCT
ejpam-1854	173	1	77/1	77/1	NUM
ejpam-1854	173	2	-	-	SYM
ejpam-1854	173	3	2	2	NUM
ejpam-1854	173	4	,	,	PUNCT
ejpam-1854	173	5	39	39	NUM
ejpam-1854	173	6	-	-	SYM
ejpam-1854	173	7	63	63	NUM
ejpam-1854	173	8	.	.	PUNCT
ejpam-1854	174	1	2010	2010	NUM
ejpam-1854	174	2	.	.	PUNCT
ejpam-1854	175	1	[	[	X
ejpam-1854	175	2	12	12	NUM
ejpam-1854	175	3	]	]	X
ejpam-1854	175	4	w.j	w.j	PROPN
ejpam-1854	175	5	.	.	PROPN
ejpam-1854	175	6	leveque	leveque	ADJ
ejpam-1854	175	7	.	.	PUNCT
ejpam-1854	176	1	on	on	ADP
ejpam-1854	176	2	mahler	mahler	PROPN
ejpam-1854	176	3	’s	’s	PART
ejpam-1854	176	4	unumbers	unumber	NOUN
ejpam-1854	176	5	.	.	PUNCT
ejpam-1854	177	1	london	london	PROPN
ejpam-1854	177	2	mathematical	mathematical	ADJ
ejpam-1854	177	3	society	society	NOUN
ejpam-1854	177	4	.	.	PUNCT
ejpam-1854	178	1	220	220	NUM
ejpam-1854	178	2	-229	-229	NOUN
ejpam-1854	178	3	.	.	PROPN
ejpam-1854	178	4	1953	1953	NUM
ejpam-1854	178	5	.	.	PUNCT
ejpam-1854	179	1	[	[	X
ejpam-1854	179	2	13	13	NUM
ejpam-1854	179	3	]	]	X
ejpam-1854	179	4	x.x	x.x	PROPN
ejpam-1854	179	5	.	.	PUNCT
ejpam-1854	180	1	long	long	ADJ
ejpam-1854	180	2	.	.	PUNCT
ejpam-1854	181	1	mahler	mahler	PROPN
ejpam-1854	181	2	’s	’s	PART
ejpam-1854	181	3	classification	classification	NOUN
ejpam-1854	181	4	of	of	ADP
ejpam-1854	181	5	p	p	NOUN
ejpam-1854	181	6	-	-	PUNCT
ejpam-1854	181	7	adic	adic	ADJ
ejpam-1854	181	8	numbers	number	NOUN
ejpam-1854	181	9	pure	pure	ADJ
ejpam-1854	181	10	and	and	CCONJ
ejpam-1854	181	11	applied	applied	ADJ
ejpam-1854	181	12	mathematics	mathematic	NOUN
ejpam-1854	181	13	.	.	PUNCT
ejpam-1854	182	1	5	5	NUM
ejpam-1854	182	2	,	,	PUNCT
ejpam-1854	182	3	73	73	NUM
ejpam-1854	182	4	80	80	NUM
ejpam-1854	182	5	.	.	PUNCT
ejpam-1854	183	1	1989	1989	NUM
ejpam-1854	183	2	.	.	PUNCT
ejpam-1854	184	1	[	[	X
ejpam-1854	184	2	14	14	NUM
ejpam-1854	184	3	]	]	PUNCT
ejpam-1854	184	4	k.	k.	PROPN
ejpam-1854	184	5	mahler	mahler	PROPN
ejpam-1854	184	6	.	.	PUNCT
ejpam-1854	185	1	zur	zur	PROPN
ejpam-1854	185	2	approximation	approximation	NOUN
ejpam-1854	185	3	der	der	NOUN
ejpam-1854	185	4	exponential	exponential	NOUN
ejpam-1854	185	5	funktion	funktion	PROPN
ejpam-1854	185	6	und	und	PROPN
ejpam-1854	185	7	des	des	PROPN
ejpam-1854	185	8	logarithmus	logarithmus	PROPN
ejpam-1854	185	9	i	i	PROPN
ejpam-1854	185	10	,	,	PUNCT
ejpam-1854	185	11	ii	ii	PROPN
ejpam-1854	185	12	,	,	PUNCT
ejpam-1854	185	13	die	die	VERB
ejpam-1854	185	14	journal	journal	PROPN
ejpam-1854	185	15	für	für	PROPN
ejpam-1854	185	16	die	die	VERB
ejpam-1854	185	17	riene	riene	PROPN
ejpam-1854	185	18	und	und	PROPN
ejpam-1854	185	19	angewandte	angewandte	PROPN
ejpam-1854	185	20	mathematik	mathematik	PROPN
ejpam-1854	185	21	.	.	PROPN
ejpam-1854	186	1	166	166	NUM
ejpam-1854	186	2	,	,	PUNCT
ejpam-1854	186	3	118150	118150	NUM
ejpam-1854	186	4	.	.	PUNCT
ejpam-1854	187	1	1932	1932	NUM
ejpam-1854	187	2	.	.	PUNCT
ejpam-1854	188	1	[	[	X
ejpam-1854	188	2	15	15	NUM
ejpam-1854	188	3	]	]	X
ejpam-1854	188	4	k.	k.	PROPN
ejpam-1854	188	5	mahler	mahler	PROPN
ejpam-1854	188	6	.	.	PUNCT
ejpam-1854	189	1	uber	uber	PROPN
ejpam-1854	189	2	eine	eine	PROPN
ejpam-1854	189	3	klassen	klassen	PROPN
ejpam-1854	189	4	-	-	PUNCT
ejpam-1854	189	5	einteilung	einteilung	PROPN
ejpam-1854	189	6	der	der	NOUN
ejpam-1854	189	7	p	p	PROPN
ejpam-1854	189	8	-	-	PUNCT
ejpam-1854	189	9	adischen	adischen	NOUN
ejpam-1854	189	10	zahlen	zahlen	PROPN
ejpam-1854	189	11	,	,	PUNCT
ejpam-1854	189	12	mathematica	mathematica	PROPN
ejpam-1854	189	13	leiden	leiden	PROPN
ejpam-1854	189	14	.	.	PUNCT
ejpam-1854	190	1	3	3	NUM
ejpam-1854	190	2	,	,	PUNCT
ejpam-1854	190	3	177	177	NUM
ejpam-1854	190	4	-	-	SYM
ejpam-1854	190	5	185	185	NUM
ejpam-1854	190	6	.	.	PUNCT
ejpam-1854	191	1	1935	1935	NUM
ejpam-1854	191	2	.	.	PUNCT
ejpam-1854	192	1	[	[	X
ejpam-1854	192	2	16	16	NUM
ejpam-1854	192	3	]	]	PUNCT
ejpam-1854	192	4	k.	k.	PROPN
ejpam-1854	192	5	mahler	mahler	PROPN
ejpam-1854	192	6	.	.	PUNCT
ejpam-1854	193	1	on	on	ADP
ejpam-1854	193	2	a	a	DET
ejpam-1854	193	3	theorem	theorem	NOUN
ejpam-1854	193	4	of	of	ADP
ejpam-1854	193	5	liouville	liouville	NOUN
ejpam-1854	193	6	in	in	ADP
ejpam-1854	193	7	fields	field	NOUN
ejpam-1854	193	8	of	of	ADP
ejpam-1854	193	9	positive	positive	ADJ
ejpam-1854	193	10	characteristic	characteristic	NOUN
ejpam-1854	193	11	.	.	PUNCT
ejpam-1854	194	1	canadian	canadian	ADJ
ejpam-1854	194	2	journal	journal	PROPN
ejpam-1854	194	3	of	of	ADP
ejpam-1854	194	4	mathematics	mathematic	NOUN
ejpam-1854	194	5	.	.	PUNCT
ejpam-1854	195	1	1	1	NUM
ejpam-1854	195	2	,	,	PUNCT
ejpam-1854	195	3	397	397	NUM
ejpam-1854	195	4	-	-	SYM
ejpam-1854	195	5	400	400	NUM
ejpam-1854	195	6	.	.	PUNCT
ejpam-1854	196	1	1949	1949	NUM
ejpam-1854	196	2	.	.	PUNCT
ejpam-1854	197	1	[	[	X
ejpam-1854	197	2	17	17	NUM
ejpam-1854	197	3	]	]	X
ejpam-1854	197	4	h.	h.	PROPN
ejpam-1854	197	5	menken	menken	PROPN
ejpam-1854	197	6	.	.	PUNCT
ejpam-1854	198	1	an	an	DET
ejpam-1854	198	2	investigation	investigation	NOUN
ejpam-1854	198	3	on	on	ADP
ejpam-1854	198	4	p	p	NOUN
ejpam-1854	198	5	-	-	PUNCT
ejpam-1854	198	6	adic	adic	ADJ
ejpam-1854	198	7	u	u	NOUN
ejpam-1854	198	8	numbers	number	NOUN
ejpam-1854	198	9	,	,	PUNCT
ejpam-1854	198	10	university	university	PROPN
ejpam-1854	198	11	of	of	ADP
ejpam-1854	198	12	istanbul	istanbul	PROPN
ejpam-1854	198	13	faculty	faculty	PROPN
ejpam-1854	198	14	of	of	ADP
ejpam-1854	198	15	science	science	PROPN
ejpam-1854	198	16	journal	journal	PROPN
ejpam-1854	198	17	of	of	ADP
ejpam-1854	198	18	mathematics	mathematic	NOUN
ejpam-1854	198	19	.	.	PUNCT
ejpam-1854	199	1	59	59	NUM
ejpam-1854	199	2	,	,	PUNCT
ejpam-1854	199	3	111	111	NUM
ejpam-1854	199	4	-	-	SYM
ejpam-1854	199	5	143	143	NUM
ejpam-1854	199	6	.	.	PUNCT
ejpam-1854	199	7	2000	2000	NUM
ejpam-1854	199	8	.	.	PUNCT
ejpam-1854	200	1	[	[	X
ejpam-1854	200	2	18	18	NUM
ejpam-1854	200	3	]	]	X
ejpam-1854	200	4	h.	h.	PROPN
ejpam-1854	200	5	menken	menken	PROPN
ejpam-1854	200	6	,	,	PUNCT
ejpam-1854	200	7	and	and	CCONJ
ejpam-1854	200	8	k.r	k.r	PROPN
ejpam-1854	200	9	.	.	PROPN
ejpam-1854	200	10	mamedov	mamedov	PROPN
ejpam-1854	200	11	.	.	PUNCT
ejpam-1854	201	1	point	point	NOUN
ejpam-1854	201	2	on	on	ADP
ejpam-1854	201	3	curves	curve	NOUN
ejpam-1854	201	4	whose	whose	DET
ejpam-1854	201	5	coordinates	coordinate	NOUN
ejpam-1854	201	6	are	be	AUX
ejpam-1854	201	7	p	p	ADJ
ejpam-1854	201	8	-	-	PUNCT
ejpam-1854	201	9	adic	adic	ADJ
ejpam-1854	201	10	unumbers	unumber	NOUN
ejpam-1854	201	11	,	,	PUNCT
ejpam-1854	201	12	p	p	ADJ
ejpam-1854	201	13	-	-	PUNCT
ejpam-1854	201	14	adic	adic	ADJ
ejpam-1854	201	15	mathematical	mathematical	ADJ
ejpam-1854	201	16	physics	physics	NOUN
ejpam-1854	201	17	,	,	PUNCT
ejpam-1854	201	18	267	267	NUM
ejpam-1854	201	19	-	-	SYM
ejpam-1854	201	20	273	273	NUM
ejpam-1854	201	21	,	,	PUNCT
ejpam-1854	201	22	aip	aip	PROPN
ejpam-1854	201	23	conference	conference	NOUN
ejpam-1854	201	24	proceedings	proceeding	NOUN
ejpam-1854	201	25	826	826	NUM
ejpam-1854	201	26	,	,	PUNCT
ejpam-1854	201	27	american	american	PROPN
ejpam-1854	201	28	institute	institute	PROPN
ejpam-1854	201	29	of	of	ADP
ejpam-1854	201	30	physics	physics	PROPN
ejpam-1854	201	31	,	,	PUNCT
ejpam-1854	201	32	melville	melville	PROPN
ejpam-1854	201	33	,	,	PUNCT
ejpam-1854	201	34	ny	ny	PROPN
ejpam-1854	201	35	.	.	PROPN
ejpam-1854	201	36	2006	2006	NUM
ejpam-1854	201	37	.	.	PUNCT
ejpam-1854	202	1	[	[	X
ejpam-1854	202	2	19	19	NUM
ejpam-1854	202	3	]	]	PUNCT
ejpam-1854	202	4	k.	k.	PROPN
ejpam-1854	202	5	nishioka	nishioka	PROPN
ejpam-1854	202	6	.	.	PUNCT
ejpam-1854	203	1	p	p	X
ejpam-1854	203	2	-	-	PUNCT
ejpam-1854	203	3	adic	adic	ADJ
ejpam-1854	203	4	transcendental	transcendental	ADJ
ejpam-1854	203	5	numbers	number	NOUN
ejpam-1854	203	6	,	,	PUNCT
ejpam-1854	203	7	proceedings	proceeding	NOUN
ejpam-1854	203	8	of	of	ADP
ejpam-1854	203	9	the	the	DET
ejpam-1854	203	10	american	american	PROPN
ejpam-1854	203	11	mathematical	mathematical	PROPN
ejpam-1854	203	12	society	society	NOUN
ejpam-1854	203	13	108	108	NUM
ejpam-1854	203	14	,	,	PUNCT
ejpam-1854	203	15	no.1	no.1	NUM
ejpam-1854	203	16	,	,	PUNCT
ejpam-1854	203	17	39	39	NUM
ejpam-1854	203	18	-	-	SYM
ejpam-1854	203	19	41	41	NUM
ejpam-1854	203	20	.	.	PUNCT
ejpam-1854	203	21	1990	1990	NUM
ejpam-1854	203	22	.	.	PUNCT
ejpam-1854	204	1	[	[	X
ejpam-1854	204	2	20	20	NUM
ejpam-1854	204	3	]	]	PUNCT
ejpam-1854	204	4	m.	m.	NOUN
ejpam-1854	204	5	van	van	PROPN
ejpam-1854	204	6	der	der	NOUN
ejpam-1854	204	7	put	put	VERB
ejpam-1854	204	8	and	and	CCONJ
ejpam-1854	204	9	l.	l.	PROPN
ejpam-1854	204	10	taelman	taelman	PROPN
ejpam-1854	204	11	.	.	PUNCT
ejpam-1854	205	1	local	local	ADJ
ejpam-1854	205	2	p	p	ADJ
ejpam-1854	205	3	-	-	PUNCT
ejpam-1854	205	4	adic	adic	ADJ
ejpam-1854	205	5	differential	differential	NOUN
ejpam-1854	205	6	equations	equation	NOUN
ejpam-1854	205	7	,	,	PUNCT
ejpam-1854	205	8	p	p	ADJ
ejpam-1854	205	9	-	-	PUNCT
ejpam-1854	205	10	adic	adic	ADJ
ejpam-1854	205	11	mathematical	mathematical	ADJ
ejpam-1854	205	12	physics	physics	NOUN
ejpam-1854	205	13	,	,	PUNCT
ejpam-1854	205	14	291	291	NUM
ejpam-1854	205	15	-	-	SYM
ejpam-1854	205	16	297	297	NUM
ejpam-1854	205	17	,	,	PUNCT
ejpam-1854	205	18	aip	aip	PROPN
ejpam-1854	205	19	conference	conference	NOUN
ejpam-1854	205	20	proceedings	proceeding	NOUN
ejpam-1854	205	21	826	826	NUM
ejpam-1854	205	22	,	,	PUNCT
ejpam-1854	205	23	american	american	PROPN
ejpam-1854	205	24	institute	institute	PROPN
ejpam-1854	205	25	of	of	ADP
ejpam-1854	205	26	physics	physics	PROPN
ejpam-1854	205	27	,	,	PUNCT
ejpam-1854	205	28	melville	melville	PROPN
ejpam-1854	205	29	,	,	PUNCT
ejpam-1854	205	30	ny	ny	PROPN
ejpam-1854	205	31	.	.	PROPN
ejpam-1854	205	32	2006	2006	NUM
ejpam-1854	205	33	.	.	PUNCT
ejpam-1854	206	1	[	[	X
ejpam-1854	206	2	21	21	NUM
ejpam-1854	206	3	]	]	X
ejpam-1854	206	4	w.h	w.h	PROPN
ejpam-1854	206	5	.	.	PROPN
ejpam-1854	206	6	schikhof	schikhof	PROPN
ejpam-1854	206	7	.	.	PUNCT
ejpam-1854	206	8	ultrametric	ultrametric	ADJ
ejpam-1854	206	9	calculus	calculus	NOUN
ejpam-1854	206	10	,	,	PUNCT
ejpam-1854	206	11	cambridge	cambridge	PROPN
ejpam-1854	206	12	university	university	PROPN
ejpam-1854	206	13	press	press	PROPN
ejpam-1854	206	14	,	,	PUNCT
ejpam-1854	206	15	cambridge	cambridge	PROPN
ejpam-1854	206	16	.	.	PUNCT
ejpam-1854	206	17	2006	2006	NUM
ejpam-1854	206	18	.	.	PUNCT