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Functional relations and special values of Mordell-Tornheim triple zeta and  -functions
Author(s):
Kohji
Matsumoto;
Takashi
Nakamura;
Hirofumi
Tsumura
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2135-2145.
MSC (2000):
Primary 40B05;
Secondary 11M35, 11M06, 33E20
Posted:
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  -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  -functions.
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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
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
DOI:
10.1090/S0002-9939-08-09192-2
PII:
S 0002-9939(08)09192-2
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
Posted:
February 21, 2008
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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