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arXiv · 0812.0385

The ubiquitous $ζ$-function and some of its "usual" and "unusual" meromorphic properties

Klaus Kirsten·Paul Loya·Jinsung Park
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Abstract

In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions of these $\z$-functions have, in general, countably many logarithmic branch cuts on the nonpositive real axis and unusual locations of poles with arbitrarily large multiplicity. Moreover, we give a precise algebraic-combinatorial formula to compute the coefficients of the leading order terms of the singularities.

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Klaus Kirsten, Paul Loya, Jinsung Park. 2008-12-01. The ubiquitous $ζ$-function and some of its "usual" and "unusual" meromorphic properties. https://doi.org/10.1088/1751-8113/41/16/164070

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