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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