The Selberg Trace Formula and Selberg Zeta-function for Cofinite Kleinian Groups with Finite-dimensional Unitary Representations

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of Elstrodt, Grunewald and Mennicke to non-trivial unitary representations. We show that the presence of cuspidal elliptic… CONTINUE READING