Geometric zeta-functions of locally symmetric spaces

TL;DR

This paper generalizes the theory of geometric zeta functions to higher rank locally symmetric spaces, providing analytic continuation, divisor descriptions, and extending the zeta functions to higher-dimensional flats.

Contribution

It introduces a comprehensive generalization of geometric zeta functions for higher rank spaces, including analytic continuation and cohomological descriptions.

Findings

Analytic continuation of zeta functions established

Divisors described via tangential and group cohomology

Extended zeta functions to higher-dimensional flats

Abstract

The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in terms of tangential cohomology and in terms of group cohomology which generalizes the Patterson conjecture. We also extend the range of zeta functions in considering higher dimensional flats.