Weighted Zeta Functions - Meromorphic Continuation & Numerical Investigation

Philipp Schuette

We present work related to weighted generalizations of zeta functions for open hyperbolic systems. Particular examples of such systems are given by Schottky surfaces and strictly convex obstacle scattering. Then we sketch meromorphic continuation, which uses a trace formula and techniques of microlocal analysis. Finally, we discuss numerical applications of our weighted zeta functions to invariant Ruelle distributions in the context of Schottky surfaces.