  We study Selberg zeta functions $Z(s,\sigma)$ associated to locally
homogeneous vector bundles over the unit-sphere bundle of a complete
odd-dimensional hyperbolic manifold of finite volume. We assume a certain
condition on the fundamental group of the manifold. A priori, the Selberg zeta
functions are defined only for s in some right half-space of $\mathbb{C}$. We
will prove that for any locally homogeneous bundle the functions $Z(s,\sigma)$
have a meromorphic continuation to $\mathbb{C}$ and we will give a complete
description of their singularities in terms of spectral data of the underlying
manifold. Our work generalizes results of Bunke and Olbrich to the non-compact
situation. As an application of our results one can compare the normalized
Reidemeister torsions on hyperbolic 3 manifolds with cusps which were
introduced by Menal-Ferrer and Porti to the corresponding regularized analytic
torsions.
