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

被引：1
作者：
Xiaosheng Wu
机构：
[1] Hefei University of Technology,School of Mathematics
来源：
Mathematische Zeitschrift | 2019年 / 293卷
关键词：
Twisted second moment; Kloosterman sum; Simple zeros; Riemann zeta-function; Dirichlet ; -function; 11M26; 11M06;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：825 / 865
页数：40
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