English

Zeta functions in higher Teichmuller theory

Dynamical Systems 2024-01-09 v2

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.

Keywords

Cite

@article{arxiv.2203.15741,
  title  = {Zeta functions in higher Teichmuller theory},
  author = {Mark Pollicott and Richard Sharp},
  journal= {arXiv preprint arXiv:2203.15741},
  year   = {2024}
}

Comments

This version corresponds to the final accepted version by Mathematische Zeitschrift

R2 v1 2026-06-24T10:30:36.378Z