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Analytic Continuation of the Doubly-periodic Barnes Zeta Function

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.

preprint2013arXivOpen access
Guglielmo FucciKlaus Kirsten
math.CVmath-phmath.MP
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Guglielmo FucciKlaus Kirsten

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