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

共 50 条

[41] Ramanujan's Eisenstein series of level 7 and 14
Vasuki, K. R.
Veeresha, R. G.
JOURNAL OF NUMBER THEORY, 2016, 159 : 59 - 75
[42] On Ramanujan's Eisenstein series of level 5 and 7
Pushpa, K.
Vasuki, K. R.
JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 2022, 37 (03) : 257 - 272
[43] Double Eisenstein series and modular forms of level 4
Kina, Katsumi
RAMANUJAN JOURNAL, 2024, 65 (04): : 1651 - 1696
[44] On a Ramanujan's Eisenstein series identity of level fifteen
Bhuvan, E. N.
Vasuki, K. R.
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2019, 129 (04):
[45] CHARACTER ANALOGUES OF INFINITE SERIES IDENTITIES RELATED TO GENERALIZED NON-HOLOMORPHIC EISENSTEIN SERIES
Lim, Sung Geun
KOREAN JOURNAL OF MATHEMATICS, 2022, 30 (01): : 25 - 42
[46] ON EISENSTEIN SERIES OF DEGREE-2
KITAOKA, Y
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1987, 63 (04) : 114 - 117
[47] EISENSTEIN SERIES OF WEIGHT 3/2
PEI, DY
KEXUE TONGBAO, 1983, 28 (02): : 282 - 282
[48] Eisenstein series associated with Γ0(2)
Heekyoung Hahn
The Ramanujan Journal, 2008, 15 : 235 - 257
[49] Eisenstein series associated with Γ0(2)
Hahn, Heekyoung
RAMANUJAN JOURNAL, 2008, 15 (02): : 235 - 257
[50] ON HERMITIAN EISENSTEIN SERIES OF DEGREE 2
Hauffe-waschbuesch, Adrian
Krieg, Aloys
Williams, Brandon
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2023, 68 (01) : 127 - 141

← 1 2 3 4 5 →