An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers

被引：10

作者：

Komori, Yasushi ^{[1
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

来源：

RAMANUJAN JOURNAL | 2008年 / 17卷 / 02期

关键词：

Mordell-Tornheim double zeta function; Analytic continuation; Integral representation;

D O I：

10.1007/s11139-008-9130-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A surface integral representation of the Mordell-Tornheim double zeta function is given, which is a direct analogue of a well-known integral representation of the Riemann zeta function of Hankel's type. As an application, we investigate its values and residues at integers, where generalizations of a generating function of Bernoulli numbers naturally appear.

引用

页码：163 / 183

页数：21

共 14 条

[1] An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers
Yasushi Komori
The Ramanujan Journal, 2008, 17
[2] Mordell-Tornheim multiple zeta values at non-positive integers
Onodera, Kazuhiro
RAMANUJAN JOURNAL, 2013, 32 (02): : 221 - 226
[3] Mean value theorems for the Mordell-Tornheim double zeta-function
Okamoto, Takuya
Onozuka, Tomokazu
RAMANUJAN JOURNAL, 2015, 37 (01): : 131 - 163
[4] Multiple zeta values at the non-positive integers
Sadaoui, Boualem
COMPTES RENDUS MATHEMATIQUE, 2014, 352 (12) : 977 - 984
[5] Reducibility of signed cyclic sums of Mordell-Tornheim zeta and L-values
Zhao, Jianqiang
Zhou, Xia
JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 2011, 26 (04) : 383 - 414
[6] A symbolic approach to multiple Hurwitz zeta values at non-positive integers
Sadaoui, Boualem
Jarad, Fahd
Adjabi, Yacine
Turkan, Erkan Murat
OPEN MATHEMATICS, 2023, 21 (01):
[7] Multiple zeta values for coordinatewise limits at non-positive integers
Sasaki, Yoshitaka
ACTA ARITHMETICA, 2009, 136 (04) : 299 - 317
[8] The first derivative multiple zeta values at non-positive integers
Yoshitaka Sasaki
The Ramanujan Journal, 2010, 21 : 267 - 284
[9] The first derivative multiple zeta values at non-positive integers
Sasaki, Yoshitaka
RAMANUJAN JOURNAL, 2010, 21 (03): : 267 - 284
[10] Evaluation of multiple zeta values for various limiting processes at non-positive integers
Sasaki, Yoshitaka
RESEARCH IN NUMBER THEORY, 2023, 9 (02)

← 1 2 →