The twisted mean square and critical zeros of Dirichlet L-functions

被引：9

作者：

Wu, Xiaosheng ^{[1
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China

来源：

MATHEMATISCHE ZEITSCHRIFT | 2019年 / 293卷 / 1-2期

关键词：

Twisted second moment; Kloosterman sum; Simple zeros; Riemann zeta-function; Dirichlet L-function; RIEMANN ZETA-FUNCTION;

D O I：

10.1007/s00209-018-2209-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we obtain an asymptotic formula for the twisted mean square of a Dirichlet L-function with a longer mollifier, whose coefficients are also more general than before. As an application we obtain that, for every Dirichlet L-function, more than 41.72% of zeros are on the critical line and more than 40.74% of zeros are simple and on the critical line. These proportions also improve previous results which were proved only for the Riemann zeta-function.

引用

页码：825 / 865

页数：41

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