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.
"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