On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces

TL;DR

This paper derives approximate formulas for the logarithmic derivatives of Selberg and Ruelle zeta functions on compact, even-dimensional, locally symmetric spaces of rank one, expressed through their singularities.

Contribution

It provides new approximate formulas for the logarithmic derivatives of zeta functions in the context of compact, even-dimensional, locally symmetric spaces of rank one.

Findings

Formulas expressed in terms of zeta-singularities

Applicable to compact, even-dimensional, locally symmetric spaces of rank one

Advances understanding of zeta function behavior in geometric analysis

Abstract

We derive approximate formulas for the logarithmic de- rivative of the Selberg and Ruelle zeta functions over compact, even- dimensional, locally symmetric spaces of rank one. The obtained for- mulas are given in terms of the zeta-singularities.