DISTINCT ZEROS AND SIMPLE ZEROS FOR THE FAMILY OF DIRICHLET L-FUNCTIONS

被引：4

作者：

Wu, Xiaosheng ^{[1
]}

机构：

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

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2016年 / 67卷 / 04期

关键词：

RIEMANN ZETA-FUNCTION; CRITICAL LINE;

D O I：

10.1093/qmath/haw039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

this paper, we study the number of additional zeros of Dirichlet L-function caused by multiplicity by using Asymptotic Large Sieve. Then in asymptotic terms we prove that there are > 80.13% of zeros of the family of Dirichlet L-functions which are distinct and > 60.261% of zeros of the family of Dirichlet L-functions which are simple. In addition, assuming the Generalized Riemann Hypothesis, we improve these proportions to 83.216% and 66.433%.

引用

页码：757 / 779

页数：23

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