id	sid	tid	token	lemma	pos
8s45q813k6n	1	1	let	let	VERB
8s45q813k6n	1	2	ì¢è	ì¢è	PROPN
8s45q813k6n	1	3	 	 	SPACE
8s45q813k6n	1	4	'	'	NOUN
8s45q813k6n	1	5	_	_	PROPN
8s45q813k6n	1	6	z	z	X
8s45q813k6n	1	7	be	be	AUX
8s45q813k6n	1	8	the	the	DET
8s45q813k6n	1	9	cauchy	cauchy	ADJ
8s45q813k6n	1	10	-	-	PUNCT
8s45q813k6n	1	11	riemann	riemann	NOUN
8s45q813k6n	1	12	operator	operator	NOUN
8s45q813k6n	1	13	and	and	CCONJ
8s45q813k6n	1	14	f	f	X
8s45q813k6n	1	15	be	be	AUX
8s45q813k6n	1	16	a	a	DET
8s45q813k6n	1	17	real	real	ADV
8s45q813k6n	1	18	-	-	PUNCT
8s45q813k6n	1	19	valued	value	VERB
8s45q813k6n	1	20	cn	cn	PROPN
8s45q813k6n	1	21	function	function	NOUN
8s45q813k6n	1	22	in	in	ADP
8s45q813k6n	1	23	a	a	DET
8s45q813k6n	1	24	neighborhood	neighborhood	NOUN
8s45q813k6n	1	25	of	of	ADP
8s45q813k6n	1	26	the	the	DET
8s45q813k6n	1	27	origin	origin	NOUN
8s45q813k6n	1	28	in	in	ADP
8s45q813k6n	1	29	the	the	DET
8s45q813k6n	1	30	complex	complex	ADJ
8s45q813k6n	1	31	plane	plane	NOUN
8s45q813k6n	1	32	for	for	ADP
8s45q813k6n	1	33	which	which	PRON
8s45q813k6n	1	34	the	the	DET
8s45q813k6n	1	35	nth	nth	NOUN
8s45q813k6n	1	36	order	order	NOUN
8s45q813k6n	1	37	cauchy	cauchy	ADJ
8s45q813k6n	1	38	-	-	PUNCT
8s45q813k6n	1	39	riemann	riemann	NOUN
8s45q813k6n	1	40	derivative	derivative	NOUN
8s45q813k6n	1	41	of	of	ADP
8s45q813k6n	1	42	f	f	PROPN
8s45q813k6n	1	43	is	be	AUX
8s45q813k6n	1	44	non	non	ADJ
8s45q813k6n	1	45	-	-	ADJ
8s45q813k6n	1	46	zero	zero	NUM
8s45q813k6n	1	47	for	for	ADP
8s45q813k6n	1	48	all	all	DET
8s45q813k6n	1	49	z	z	PROPN
8s45q813k6n	1	50	other	other	ADJ
8s45q813k6n	1	51	than	than	ADP
8s45q813k6n	1	52	0	0	NUM
8s45q813k6n	1	53	in	in	ADP
8s45q813k6n	1	54	that	that	DET
8s45q813k6n	1	55	neighborhood	neighborhood	NOUN
8s45q813k6n	1	56	.	.	PUNCT
8s45q813k6n	2	1	carathìäå	carathìäå	PROPN
8s45q813k6n	2	2	©	©	PROPN
8s45q813k6n	2	3	odory	odory	PROPN
8s45q813k6n	2	4	conjectured	conjecture	VERB
8s45q813k6n	2	5	that	that	SCONJ
8s45q813k6n	2	6	a	a	DET
8s45q813k6n	2	7	sphere	sphere	NOUN
8s45q813k6n	2	8	immersed	immerse	VERB
8s45q813k6n	2	9	in	in	ADP
8s45q813k6n	2	10	r3	r3	PROPN
8s45q813k6n	2	11	must	must	AUX
8s45q813k6n	2	12	have	have	VERB
8s45q813k6n	2	13	at	at	ADV
8s45q813k6n	2	14	least	least	ADV
8s45q813k6n	2	15	two	two	NUM
8s45q813k6n	2	16	umbilics	umbilic	NOUN
8s45q813k6n	2	17	.	.	PUNCT
8s45q813k6n	3	1	this	this	DET
8s45q813k6n	3	2	later	later	ADV
8s45q813k6n	3	3	motivated	motivated	ADJ
8s45q813k6n	3	4	loewner	loewner	NOUN
8s45q813k6n	3	5	to	to	PART
8s45q813k6n	3	6	conjecture	conjecture	VERB
8s45q813k6n	3	7	an	an	DET
8s45q813k6n	3	8	upper	upper	ADJ
8s45q813k6n	3	9	bound	bound	NOUN
8s45q813k6n	3	10	of	of	ADP
8s45q813k6n	3	11	n	n	NOUN
8s45q813k6n	3	12	for	for	ADP
8s45q813k6n	3	13	the	the	DET
8s45q813k6n	3	14	index	index	NOUN
8s45q813k6n	3	15	of	of	ADP
8s45q813k6n	3	16	the	the	DET
8s45q813k6n	3	17	nth	nth	NOUN
8s45q813k6n	3	18	order	order	NOUN
8s45q813k6n	3	19	cauchy	cauchy	ADJ
8s45q813k6n	3	20	-	-	PUNCT
8s45q813k6n	3	21	riemann	riemann	NOUN
8s45q813k6n	3	22	derivative	derivative	NOUN
8s45q813k6n	3	23	of	of	ADP
8s45q813k6n	3	24	f	f	PROPN
8s45q813k6n	3	25	as	as	ADP
8s45q813k6n	3	26	a	a	DET
8s45q813k6n	3	27	vector	vector	NOUN
8s45q813k6n	3	28	fields	field	NOUN
8s45q813k6n	3	29	.	.	PUNCT
8s45q813k6n	4	1	both	both	PRON
8s45q813k6n	4	2	of	of	ADP
8s45q813k6n	4	3	these	these	DET
8s45q813k6n	4	4	conjectures	conjecture	NOUN
8s45q813k6n	4	5	remain	remain	VERB
8s45q813k6n	4	6	open	open	ADJ
8s45q813k6n	4	7	.	.	PUNCT
8s45q813k6n	5	1	recent	recent	ADJ
8s45q813k6n	5	2	work	work	NOUN
8s45q813k6n	5	3	of	of	ADP
8s45q813k6n	5	4	f.	f.	PROPN
8s45q813k6n	5	5	xavier	xavier	PROPN
8s45q813k6n	5	6	produced	produce	VERB
8s45q813k6n	5	7	a	a	DET
8s45q813k6n	5	8	formula	formula	NOUN
8s45q813k6n	5	9	for	for	ADP
8s45q813k6n	5	10	computing	compute	VERB
8s45q813k6n	5	11	the	the	DET
8s45q813k6n	5	12	index	index	NOUN
8s45q813k6n	5	13	of	of	ADP
8s45q813k6n	5	14	such	such	ADJ
8s45q813k6n	5	15	vector	vector	NOUN
8s45q813k6n	5	16	fields	field	NOUN
8s45q813k6n	5	17	in	in	ADP
8s45q813k6n	5	18	the	the	DET
8s45q813k6n	5	19	case	case	NOUN
8s45q813k6n	5	20	n	n	ADP
8s45q813k6n	5	21	=	=	SYM
8s45q813k6n	5	22	2	2	NUM
8s45q813k6n	5	23	using	use	VERB
8s45q813k6n	5	24	data	datum	NOUN
8s45q813k6n	5	25	about	about	ADP
8s45q813k6n	5	26	the	the	DET
8s45q813k6n	5	27	hessian	hessian	PROPN
8s45q813k6n	5	28	of	of	ADP
8s45q813k6n	5	29	f.	f.	PROPN
8s45q813k6n	5	30	in	in	ADP
8s45q813k6n	5	31	this	this	DET
8s45q813k6n	5	32	paper	paper	NOUN
8s45q813k6n	5	33	,	,	PUNCT
8s45q813k6n	5	34	we	we	PRON
8s45q813k6n	5	35	extend	extend	VERB
8s45q813k6n	5	36	this	this	DET
8s45q813k6n	5	37	result	result	NOUN
8s45q813k6n	5	38	and	and	CCONJ
8s45q813k6n	5	39	establish	establish	VERB
8s45q813k6n	5	40	an	an	DET
8s45q813k6n	5	41	index	index	NOUN
8s45q813k6n	5	42	formula	formula	NOUN
8s45q813k6n	5	43	for	for	ADP
8s45q813k6n	5	44	the	the	DET
8s45q813k6n	5	45	nth	nth	PROPN
8s45q813k6n	5	46	order	order	NOUN
8s45q813k6n	5	47	cauchy	cauchy	ADJ
8s45q813k6n	5	48	-	-	PUNCT
8s45q813k6n	5	49	riemann	riemann	NOUN
8s45q813k6n	5	50	derivative	derivative	NOUN
8s45q813k6n	5	51	that	that	PRON
8s45q813k6n	5	52	is	be	AUX
8s45q813k6n	5	53	valid	valid	ADJ
8s45q813k6n	5	54	for	for	ADP
8s45q813k6n	5	55	all	all	DET
8s45q813k6n	5	56	n	n	ADP
8s45q813k6n	5	57	ì¢'¡å	ì¢'¡å	SPACE
8s45q813k6n	5	58	´	´	PROPN
8s45q813k6n	5	59	2	2	NUM
8s45q813k6n	5	60	.	.	PUNCT
8s45q813k6n	5	61	structurally	structurally	PROPN
8s45q813k6n	5	62	,	,	PUNCT
8s45q813k6n	5	63	our	our	PRON
8s45q813k6n	5	64	index	index	NOUN
8s45q813k6n	5	65	formula	formula	NOUN
8s45q813k6n	5	66	provides	provide	VERB
8s45q813k6n	5	67	a	a	DET
8s45q813k6n	5	68	defect	defect	ADJ
8s45q813k6n	5	69	term	term	NOUN
8s45q813k6n	5	70	for	for	ADP
8s45q813k6n	5	71	loewner	loewner	NOUN
8s45q813k6n	5	72	's	's	PART
8s45q813k6n	5	73	conjecture	conjecture	NOUN
8s45q813k6n	5	74	containing	contain	VERB
8s45q813k6n	5	75	geometric	geometric	ADJ
8s45q813k6n	5	76	data	datum	NOUN
8s45q813k6n	5	77	extracted	extract	VERB
8s45q813k6n	5	78	from	from	ADP
8s45q813k6n	5	79	hessian	hessian	ADJ
8s45q813k6n	5	80	-	-	PUNCT
8s45q813k6n	5	81	like	like	ADJ
8s45q813k6n	5	82	objects	object	NOUN
8s45q813k6n	5	83	associated	associate	VERB
8s45q813k6n	5	84	with	with	ADP
8s45q813k6n	5	85	higher	high	ADJ
8s45q813k6n	5	86	order	order	NOUN
8s45q813k6n	5	87	derivatives	derivative	NOUN
8s45q813k6n	5	88	of	of	ADP
8s45q813k6n	5	89	f.	f.	PROPN
8s45q813k6n	5	90	in	in	ADP
8s45q813k6n	5	91	particular	particular	ADJ
8s45q813k6n	5	92	,	,	PUNCT
8s45q813k6n	5	93	our	our	PRON
8s45q813k6n	5	94	index	index	NOUN
8s45q813k6n	5	95	formula	formula	NOUN
8s45q813k6n	5	96	computes	compute	VERB
8s45q813k6n	5	97	the	the	DET
8s45q813k6n	5	98	fredholm	fredholm	PROPN
8s45q813k6n	5	99	index	index	NOUN
8s45q813k6n	5	100	of	of	ADP
8s45q813k6n	5	101	the	the	DET
8s45q813k6n	5	102	toeplitz	toeplitz	NOUN
8s45q813k6n	5	103	operator	operator	NOUN
8s45q813k6n	5	104	on	on	ADP
8s45q813k6n	5	105	the	the	DET
8s45q813k6n	5	106	unit	unit	NOUN
8s45q813k6n	5	107	circle	circle	NOUN
8s45q813k6n	5	108	whose	whose	DET
8s45q813k6n	5	109	symbol	symbol	NOUN
8s45q813k6n	5	110	is	be	AUX
8s45q813k6n	5	111	the	the	DET
8s45q813k6n	5	112	nth	nth	NOUN
8s45q813k6n	5	113	order	order	NOUN
8s45q813k6n	5	114	cauchy	cauchy	ADJ
8s45q813k6n	5	115	-	-	PUNCT
8s45q813k6n	5	116	riemann	riemann	NOUN
8s45q813k6n	5	117	derivative	derivative	NOUN
8s45q813k6n	5	118	of	of	ADP
8s45q813k6n	5	119	f.	f.	PROPN