Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group

TL;DR

This paper proves Patterson's conjecture regarding the singularities of the Selberg zeta function for convex-cocompact, torsion-free Kleinian groups acting on hyperbolic spaces, advancing understanding of their spectral properties.

Contribution

It establishes the conjecture connecting group cohomology with the singularities of the Selberg zeta function for a specific class of Kleinian groups.

Findings

Proof of Patterson's conjecture on singularities

Link between group cohomology and zeta function behavior

Enhanced understanding of hyperbolic group spectral theory

Abstract

We prove Patterson's conjecture about the singularities of the Selberg zeta function associated to a convex-cocompact, torsion free group acting on a hyperbolic space.