Zeta functions in higher Teichmuller theory

Abstract

In this note we introduce zeta functions and L-functions for discrete and faithful representations of surface groups in PSL(d, R), for d >= 3. These are natural generalizations of the wellknown classical Selberg zeta function and L-function for Fuchsian groups, corresponding to the case d=2.We show that these complex functions have meromorphic extensions to the entire complex plane C.

This version corresponds to the final accepted version by Mathematische Zeitschrift