## Tsukuba Journal of Mathematics

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

Takashi Miyagawa

#### 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
Revised: 14 January 2016
First available in Project Euclid: 24 September 2016

https://projecteuclid.org/euclid.tkbjm/1474747488

Digital Object Identifier
doi:10.21099/tkbjm/1474747488

Mathematical Reviews number (MathSciNet)
MR3550933

Zentralblatt MATH identifier
06642042

#### 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