Distribution of the zeta functions singularities for compact even-dimensional locally symmetric spaces

TL;DR

This paper provides precise estimates on the number of singularities of Selberg's and Ruelle's zeta functions for compact, even-dimensional, locally symmetric spaces, advancing understanding of their spectral properties.

Contribution

It offers new, exact estimates on zeta function singularities in the context of compact, even-dimensional locally symmetric spaces, extending prior theoretical work.

Findings

Derived explicit bounds on the number of singularities

Enhanced understanding of spectral properties of zeta functions

Applied to compact, even-dimensional locally symmetric spaces

Abstract

For compact, even-dimensional, locally symmetric spaces, we obtain precise estimates on the number of singularities of Selberg's and Ruelle's zeta functions considered by U. Bunke and M. Olbrich.