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

Kirsten, Klaus; Loya, Paul; Park, Jinsung

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

Authors

Kirsten, Klaus

Loya, Paul

Park, Jinsung

Description

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