Analytic Continuation of the Doubly-periodic Barnes Zeta Function
arXiv:1304.4509 · doi:10.1016/j.amc.2013.06.092
Abstract
The aim of this work is to study the analytic continuation of the doubly-periodic Barnes zeta function. By using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic Barnes zeta function to the entire complex plane in terms of a real integral containing the Hurwitz zeta function and the first Jacobi theta function. These allow us to explicitly give expressions for the derivative at all non-positive integer points.
18 pages, Latex, 3 Figures