EXPLICIT FORMULAE FOR THE MEAN VALUE OF PRODUCTS OF VALUES OF DIRICHLET L-FUNCTIONS AT POSITIVE INTEGERS

被引：0

作者：

Louboutin, Stephane R. ^{[1
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M, Marseille, France

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 11期

关键词：

Dirichlet L-functions; characters; cotangent; mean value;

D O I：

10.1090/proc/16960

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let m >= 1 be a rational integer. We give an explicit formula for the mean value 2/phi(f) Sigma(chi(-1)=(-1)m) vertical bar L(m, chi)vertical bar(2), where chi ranges over the phi(f)/2 Dirichlet characters modulo f > 2 with the same parity as m. We then adapt our proof to obtain explicit means values for products of the form L(m(1), chi(1)) ... L(m(n-1,) chi(n-1))<(L(m(n), chi(1) ... chi(n-1)))over bar>.

引用

页码：4623 / 4631

页数：9

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