In this article, we derive meromorphic continuation of multiple Lerch zeta functions by generalizing an elegant identity of Ramanujan. Further, we describe the set of all possible singularities of these functions. Finally, for the multiple Hurwitz zeta functions, we list the exact set of singularities.
"Multiple Lerch Zeta Functions and an Idea of Ramanujan." Michigan Math. J. 67 (2) 267 - 287, May 2018. https://doi.org/10.1307/mmj/1516330974