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>.
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页码：4623 / 4631
页数：9
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