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.
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页码：365 / 378
页数：14
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