Analogues of the Hurwitz Formulas for Level 2 Eisenstein Series

被引：0
作者：
Hirofumi Tsumura
机构：
[1] Tokyo Metropolitan University,Department of Mathematics and Information Sciences
来源：
Results in Mathematics | 2010年 / 58卷
关键词：
Primary 11M41; Secondary 11M99; Eisenstein series; Hurwitz numbers; hyperbolic functions; Lemniscate constant; Riemann zeta-function;
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学科分类号：
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：13
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