In this paper, we study the Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds. These zeta functions are defined on one complex variable $s$ in some right half-plane of $\mathbb{ C}$. We use the Selberg trace formula for arbitrary not neccesarily unitary representations of the fundamental group to establish the meromorphic continuation of these zeta functions to the whole complex plane.
Categories: math.SP