Functional relations and special values of Mordell-Tornheim triple zeta and $L$-functions
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- by Kohji Matsumoto, Takashi Nakamura and Hirofumi Tsumura PDF
- Proc. Amer. Math. Soc. 136 (2008), 2135-2145 Request permission
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.References
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Additional Information
- Kohji Matsumoto
- Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan
- Email: kohjimat@math.nagoya-u.ac.jp
- Takashi Nakamura
- Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan
- MR Author ID: 755913
- Email: m03024z@math.nagoya-u.ac.jp
- Hirofumi Tsumura
- Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan
- Email: tsumura@tmu.ac.jp
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2135-2145
- MSC (2000): Primary 40B05; Secondary 11M35, 11M06, 33E20
- DOI: https://doi.org/10.1090/S0002-9939-08-09192-2
- MathSciNet review: 2383519