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Functional relations and special values of Mordell-Tornheim triple zeta and  -functions |
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| Authors: | Kohji Matsumoto Takashi Nakamura Hirofumi Tsumura |
| Institution: | Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan ; Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan ; Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan |
| 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. |
| Keywords: | Triple zeta and $L$-functions Tornheim's double series Riemann's zeta-function Dirichlet $L$-functions functional relations |
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