The divisor of Selberg's zeta function for Kleinian groups

Abstract

We compute the divisor of Selberg's zeta function for convex cocompact, torsion-free discrete groups Gamma acting on a real hyperbolic space of dimension n + 1. The divisor is determined by the eigenvalues and scattering poles of the Laplacian on X = Gamma \Hn+1 together with the Euler characteristic of X compactified to a manifold with boundary. Ifn is even, the singularities of the zeta function associated to the Euler characteristic of X are identified using work of U. Bunke and M. Olbrich.