Some Notes on Identities for Dirichlet L-functions

Some Notes on Identities for Dirichlet L-functions

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摘要 Let q ≥ 3 be an integer, and χ be a Dirichlet character modulo q, L（s, χ） denote the Dirichlet L-function corresponding to χ. In this paper, we show some early information on the mean value of the Dirichlet L-functions and give some new identities forwhere a = 2, 3, or 4. Then we give general identities for the case that the integer a divides q - 1. Keywords Dirichlet L-functions, Dedekind sum, trigonometric formula, MSbius inversion formula Let q ≥ 3 be an integer, and χ be a Dirichlet character modulo q, L（s, χ） denote the Dirichlet L-function corresponding to χ. In this paper, we show some early information on the mean value of the Dirichlet L-functions and give some new identities forwhere a = 2, 3, or 4. Then we give general identities for the case that the integer a divides q - 1. Keywords Dirichlet L-functions, Dedekind sum, trigonometric formula, MSbius inversion formula

作者 Rong MA Yu Long ZHANG Melchior GRTZMANN

机构地区 School of Science The School of Electronic and Information Engineering

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第5期747-754,共8页 数学学报（英文版）

基金 Supported by Basic Research Fund of the Northwestern Polytechnical University of China(Grant Nos.JC2011023 and JC2012252)

关键词 Dirichlet L-functions Dedekind sum trigonometric formula M¨obius inversion formula Dirichlet L-functions,Dedekind sum,trigonometric formula,M¨obius inversion formula

分类号 O174 [理学—基础数学]

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Acta Mathematica Sinica,English Series

2014年第5期

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Some Notes on Identities for Dirichlet L-functions

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