Order of zeta functions for compact odd-dimensional locally symmetric spaces

TL;DR

This paper proves that the meromorphic continuations of Ruelle and Selberg zeta functions for certain compact, odd-dimensional, locally symmetric spaces have finite order, bounded by the space's dimension.

Contribution

It establishes a bound on the order of meromorphic continuations of key zeta functions in the context of odd-dimensional locally symmetric spaces.

Findings

Meromorphic continuations have finite order.

Order is bounded by the space's dimension.

Applicable to Ruelle and Selberg zeta functions.

Abstract

We prove that the meromorphic continuations of the Ruelle and Selberg zeta functions considered by Bunke and Olbrich are of finite order not larger than the dimension of the underlaying compact, odd-dimensional, locally symmetric space.