The twisted dynamical zeta functions of Ruelle and Selberg of locally symmetric spaces of rank 1 and applications

The twisted zeta functions of Ruelle and Selberg are dynamical zeta functions, which are represented by Euler-type products over the prime closed geodesics on a compact hyperbolic manifold. For locally symmetric manifolds, harmonic analysis provides a powerful tool, the Selberg trace formula, that one can use to prove the meromorphic continuation of the dynamical zeta functions. These zeta functions have been long studied by Fried, Bunke and Olbrich, Müller, Pfaff,  Fedosova and Pohl under certain assumptions for the representation of the fundamental group. In this talk, we will present some results concerning the dynamical zeta functions, which are twisted by arbitrary representations of the fundamental group and their connections to spectral and L^^2-invariants.