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July 2016 Analytic properties of generalized Mordell-Tornheim type of multiple zeta-functions and $L$-functions
Takashi Miyagawa
Tsukuba J. Math. 40(1): 81-100 (July 2016). DOI: 10.21099/tkbjm/1474747488

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. "Analytic properties of generalized Mordell-Tornheim type of multiple zeta-functions and $L$-functions." Tsukuba J. Math. 40 (1) 81 - 100, July 2016. https://doi.org/10.21099/tkbjm/1474747488

Information

Received: 11 December 2015; Revised: 14 January 2016; Published: July 2016
First available in Project Euclid: 24 September 2016

zbMATH: 06642042
MathSciNet: MR3550933
Digital Object Identifier: 10.21099/tkbjm/1474747488

Subjects:
Primary: 11M06
Secondary: 40B05

Rights: Copyright © 2016 University of Tsukuba, Institute of Mathematics

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Vol.40 • No. 1 • July 2016
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