Real zeros of Eisenstein series and Rankin-Selberg L-functions

被引：0

作者：

Bauer, C. ^{[1
]}

Wang, Y.

机构：

[1] Dolby Labs, San Francisco, CA USA

[2] Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China

来源：

ACTA MATHEMATICA HUNGARICA | 2007年 / 115卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

Eisenstein series; Rankin-Selberg; L-function;

D O I：

10.1007/s10474-007-5102-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the Eisenstein series E(z, s) have no real zeroes for s is an element of (0,1) when the value of the imaginary part of z is in the range 1/5 < Im z < 4.94. For very large and very small values of the imaginary part of z, E(z, s) have real zeros in (1/2,), i.e. GRH does not hold for the Eisenstein series. Using these properties, we prove that the Rankin-Selberg L-function attached with the Ramanujan tau-function has no real zeros in the critical strip, except at the central point s = 1/2.

引用

页码：13 / 27

页数：15

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