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arXiv · 1512.06045

Analytic properties of generalized Mordell-Tornheim type of multiple zeta-functions and L-functions

Takashi Miyagawa
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Abstract

Analytic properties of three types of multiple zeta functions, that is, the Euler-Zagier type, the Mordell-Tornheim type and the Apostol-Vu type have been studied by a lot of authors. In particular, in the study of multiple zeta functions of the Apostol-Vu type, a generalized multiple zeta function, including both the Euler-Zagier type and the Apostol-Vu type, was introduced.In this paper, similarly we consider generalized multiple zeta-functions and $ L $-functions, which include both the Euler-Zagier type and the Mordell-Tornheim type as special cases.We prove the meromorphic continuation to the multi-dimensional complex space, and give the results on possible singularities.

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Takashi Miyagawa. 2015-12-18. Analytic properties of generalized Mordell-Tornheim type of multiple zeta-functions and L-functions. https://arxiv.org/abs/1512.06045

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