Tsukuba Journal of Mathematics

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.

Article information

Source
Tsukuba J. Math., Volume 40, Number 1 (2016), 81-100.

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

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1474747488

Digital Object Identifier
doi:10.21099/tkbjm/1474747488

Mathematical Reviews number (MathSciNet)
MR3550933

Zentralblatt MATH identifier
06642042

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section)

Keywords
Multiple zeta-function Multiple $L$-function Analytic continuation

Citation

Miyagawa, Takashi. Analytic properties of generalized Mordell-Tornheim type of multiple zeta-functions and $L$-functions. Tsukuba J. Math. 40 (2016), no. 1, 81--100. doi:10.21099/tkbjm/1474747488. https://projecteuclid.org/euclid.tkbjm/1474747488


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