Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds

Abstract

In this thesis we study the Selberg and Ruelle zeta functions on compact oriented hyperbolic manifolds<br /> X of odd dimension d. We prove that they converge in some half-plane Re(s)>c and that they admit a meromorphic continuation to the whole complex plane.<br /> We also describe the singularities of the Selberg zeta function in terms of the discrete spectrum of certain differential operators on X.<br /> Furthermore, we provide functional equations relating their values at s with those at −s. The main tool that we use is the Selberg trace formula for non-unitary twists.