Meromorphic continuation of a q-analogue of multiple zeta function

TL;DR

This paper establishes the meromorphic continuation of a q-analogue of multiple zeta functions, identifies their poles and residues, and provides a matrix representation of the translation formula.

Contribution

It introduces an elementary translation formula for q-analogues of multiple zeta functions and derives their pole structure and residues using matrix methods.

Findings

Meromorphic continuation of the q-analogue established.

Pole locations and residues identified.

Matrix representation of the translation formula derived.

Abstract

In this paper, we obtain the meromorphic continuation of a q-analogue of multiple zeta function using an elementary formula called translation formula. We then obtain the matrix representation of the translation formula and using it, we locate the poles of the function and the corresponding residues. While locating the poles, we also obtain an inverse of an infinite triangular matrix in a particular case.