Geometric zeta functions with non-unitary twists

TL;DR

This paper proves that the zeta functions of Ruelle and Selberg can be extended meromorphically to the entire complex plane for all compact locally-symmetric spaces with non-unitary twists.

Contribution

It establishes the meromorphic continuation of these zeta functions in a general setting, including non-unitary twists, broadening previous results.

Findings

Zeta functions admit meromorphic continuation on the complex plane.

Applicable to all compact locally-symmetric spaces.

Works for non-unitary twists, generalizing prior work.

Abstract

It is shown that the zeta functions of Ruelle and Selberg admit analytic continuation to meromorphic functions on the plane for every compact locally-symmetric space and every non-unitary twist.