On a problem related to discrete mean values of Dirichlet L-functions

被引：4

作者：

Elma, Ertan ^{[1
]}

机构：

[1] Univ Waterloo, Dept Pure Math, 200 Univ Ave West, Waterloo, ON N2L 3G1, Canada

来源：

JOURNAL OF NUMBER THEORY | 2020年 / 217卷

关键词：

Dirichlet L-functions; Mean values; Dirichlet characters;

D O I：

10.1016/j.jnt.2020.05.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let chi be a nonprincipal Dirichlet character modulo a prime number p >= 3 of order k >= 2. Define A(p)(chi) := 1/p - 1 Sigma(1 <= N <= P-1) Sigma(1 <= n1,n2 <= N chi(n1)=chi(n2)) 1. We prove that A(p)(chi) = p(2p - 1)/6k + (k - 1) (p + 1)/12k + a(chi) p2/pi(2)k(p - 1) Sigma(k/2)(j=1)vertical bar L(1, chi(2j-1))vertical bar(2) where a(chi) := (1 - chi(-1))/2. (C) 2020 Elsevier Inc. All right reserved.

引用

页码：36 / 43

页数：8

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