Mean values of L-functions and Dedekind sums

JOURNAL OF NUMBER THEORY

卷:132

Article

Bayad, Abdelmejid¹  Raouj, Abdelaziz² 

[1] Univ Evry Val dEssonne, Dept Math, F-91037 Evry, France

[2] Univ Cadi Ayyad, Dept Math, Fac Sci Semlalia, Marrakech, Morocco

关键词: L-function;    Cotangents Dedekind-Rademacher sums;    Bernoulli polynomial;    Bernoulli number;    Jordan function;   

DOI  :  10.1016/j.jnt.2012.01.014

来源: Elsevier

【 摘 要 】

Text. For arbitrary non-negative integers a(1,) ... ,a(d) and m(1), ... ,m(d), we introduce and investigate the mean value of the product (chi) over bar (1)(a(1)) ... (chi) over bar (d)(a(d))L(m(1) + 1, chi(1)) ... L(m(d) + 1, chi(d)), such that m(1), ... ,m(d) have the same parity and chi(i)(-1) = (-1)(mi+1), i = 1, ... ,d. Using recent results of the authors on Dedekind reciprocity law we give explicit formulae for this mean. Our studies recover and improve the previous works of Walum, Louboutin, Liu and Zhang. Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=FG2aZBD3V58. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free