SIMPLE ZEROS OF MAASS L-FUNCTIONS

被引：5

作者：

Cho, Peter Jaehyun ^{[1
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2013年 / 9卷 / 01期

关键词：

Simple zero; Maass form; L-function; CRITICAL LINE; ZETA-FUNCTION; DIRICHLET SERIES; FORMS;

D O I：

10.1142/S179304211250131X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that one simple zero of a Maass L-function implies infinitely many simple zeros of the L-function. Since Strombergsson found simple zeros of three different even Maass L-functions, we know that there are at least three Maass L-functions having infinitely many simple zeros.

引用

页码：167 / 178

页数：12

共 13 条

[1] Poles of Artin L-functions and the strong Artin conjecture
Booker, AR
[J]. ANNALS OF MATHEMATICS, 2003, 158 (03) : 1089 - 1098
[2] MORE THAN 2/5 OF THE ZEROS OF THE RIEMANN ZETA-FUNCTION ARE ON THE CRITICAL LINE
CONREY, JB
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1989, 399 : 1 - 26
[3] SIMPLE ZEROS OF THE RAMANUJAN TAU-DIRICHLET SERIES
CONREY, JB
GHOSH, A
[J]. INVENTIONES MATHEMATICAE, 1988, 94 (02) : 403 - 419
[4] SIMPLE ZEROS OF THE ZETA FUNCTION OF A QUADRATIC NUMBER-FIELD .1.
CONREY, JB
GHOSH, A
GONEK, SM
[J]. INVENTIONES MATHEMATICAE, 1986, 86 (03) : 563 - 576
[5] Summation formulae for coefficients of L-functions
Friedlander, JB
Iwaniec, H
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2005, 57 (03): : 494 - 505
[6] ZEROS ON THE CRITICAL LINE FOR DIRICHLET SERIES ATTACHED TO CERTAIN CUSP FORMS
HAFNER, JL
[J]. MATHEMATISCHE ANNALEN, 1983, 264 (01) : 21 - 37
[7] ZEROS ON THE CRITICAL LINE FOR MAASS WAVE FORM L-FUNCTIONS
HAFNER, JL
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1987, 377 : 127 - 158
[8] Heath-Brown DR., 1979, B LOND MATH SOC, V11, P17, DOI DOI 10.1112/BLMS/11.1.17
[9] MORE THAN ONE THIRD OF ZEROS OF RIEMANNS ZETA-FUNCTION ARE ON SIGMA = 1-2
LEVINSON, N
[J]. ADVANCES IN MATHEMATICS, 1974, 13 (04) : 383 - 436
[10] Meurman T., 1990, C MATH SOC J BOLYAI, V1, P325

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