Analogues of the Hurwitz Formulas for Level 2 Eisenstein Series

被引：6

作者：

Tsumura, Hirofumi ^{[1
]}

机构：

[1] Tokyo Metropolitan Univ, Dept Math & Informat Sci, Tokyo 1920397, Japan

来源：

RESULTS IN MATHEMATICS | 2010年 / 58卷 / 3-4期

基金：

日本学术振兴会;

关键词：

Eisenstein series; Hurwitz numbers; hyperbolic functions; Lemniscate constant; Riemann zeta-function;

D O I：

10.1007/s00025-010-0058-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider certain double series of Eisenstein type involving hyperbolic functions, which can be regarded as analogues of the level 2 Eisenstein series. We prove some evaluation formulas for these series at positive integers which are analogues of both the Hurwitz formulas for the level 2 Eisenstein series and the classical results given by Cauchy, Lerch, Mellin and Ramanujan.

引用

页码：365 / 378

页数：14

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