Analytic Continuation of the Doubly-periodic Barnes Zeta Function
Mathematical Physics
2013-08-02 v1 Complex Variables
math.MP
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.
Keywords
Cite
@article{arxiv.1304.4509,
title = {Analytic Continuation of the Doubly-periodic Barnes Zeta Function},
author = {Guglielmo Fucci and Klaus Kirsten},
journal= {arXiv preprint arXiv:1304.4509},
year = {2013}
}
Comments
18 pages, Latex, 3 Figures