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

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.

arXiv commentPaper presented at the 8th Workshop on Quantum Field Theory under the Influence of External Conditions (Leipzig, Germany, 16-21 September, 2007)

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Cited by in corpus (3)

• A New Example of the Effects of a Singular Background on the Zeta Function
• The spectral $\zeta$-function for quasi-regular Sturm--Liouville operators
• The exotic structure of the spectral $\zeta$-function for the Schrödinger operator with Pöschl--Teller potential