Multiple Lerch zeta functions and an idea of Ramanujan

TL;DR

This paper extends Ramanujan's identity to derive the meromorphic continuation of multiple Lerch zeta functions, characterizes their singularities, and specifies the singularities for multiple Hurwitz zeta functions.

Contribution

It generalizes Ramanujan's identity to multiple Lerch zeta functions and precisely describes their singularities, including those of multiple Hurwitz zeta functions.

Findings

Meromorphic continuation of multiple Lerch zeta functions established.

Complete description of all possible singularities.

Exact singularity set for multiple Hurwitz zeta functions.

Abstract

In this article, we derive meromorphic continuation of multiple Lerch zeta functions by generalising 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.