Complete determination of the singularity structure of zeta functions

Abstract

Series of extended Epstein type provide examples of non-trivial zeta functions with important physical applications. The regular part of their analytic continuation is seen to be a convergent or an asymptotic series. Their singularity structure is completely determined in terms of the Wodzicki residue in its generalized form, which is proven to yield the residua of all the poles of the zeta function, and not just that of the rightmost pole (obtainable from the Dixmier trace). The calculation is a very down-to-earth application of these powerful functional analytical methods in physics.

LaTeX, 10 pages, a couple of typos corrected

References in corpus (4)

• Gravity, Non-Commutative Geometry and the Wodzicki Residue
• The Vacuum Energy Density for Spherical and Cylindrical Universes
• Casimir energy of a massive field in a genus-1 surface
• New Examples for Wightman Fields on a Manifold

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• Operator Product on Locally Symmetric Spaces of Rank One and the Multiplicative Anomaly
• Calculation of Ground State Energy for Confined Fermion Fields