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

Matsumoto, Kohji; Nakamura, Takashi; Tsumura, Hirofumi

doi:10.1090/S0002-9939-08-09192-2

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.

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