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Functional relations and special values of Mordell-Tornheim triple zeta and $ L$-functions

Authors: Kohji Matsumoto, Takashi Nakamura and Hirofumi Tsumura
Journal: Proc. Amer. Math. Soc. 136 (2008), 2135-2145
MSC (2000): Primary 40B05; Secondary 11M35, 11M06, 33E20
Published electronically: February 21, 2008
MathSciNet review: 2383519
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Abstract: In this paper, we prove the existence of meromorphic continuation of certain triple zeta-functions of Lerch's type. Based on this result, we prove some functional relations for triple zeta and $ L$-functions of the Mordell-Tornheim type. Using these functional relations, we prove new explicit evaluation formulas for special values of these functions. These can be regarded as triple analogues of known results for double zeta and $ L$-functions.

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Additional Information

Kohji Matsumoto
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan

Takashi Nakamura
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan

Hirofumi Tsumura
Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan

Keywords: Triple zeta and $L$-functions, Tornheim's double series, Riemann's zeta-function, Dirichlet $L$-functions, functional relations
Received by editor(s): August 31, 2006
Received by editor(s) in revised form: April 11, 2007
Published electronically: February 21, 2008
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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