On Asymptotic Behavior of Zeta Singularities for Compact Locally Symmetric Spaces

Abstract

We obtain precise estimates for the number of singularities of Selberg’s and Ruelle’s zeta functions for compact, higher-dimensional, locally symmetric Riemannian manifolds of strictly negative sectional curvature. The methods applied in this research represent a generalization of the methods described in the case of a compact Riemann surface. In particular, this includes an application of the Phragmen-Lindelof theorem, the variation of the argument of certain zeta functions, as well as the use of some classical analytic number theory techniques.