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arXiv · 1304.4509

Analytic Continuation of the Doubly-periodic Barnes Zeta Function

Guglielmo Fucci·Klaus Kirsten
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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.

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Guglielmo Fucci, Klaus Kirsten. 2013-04-16. Analytic Continuation of the Doubly-periodic Barnes Zeta Function. https://doi.org/10.1016/j.amc.2013.06.092

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