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For cofinite Kleinian groups, with finite-dimensional unitaryrepresentations, we derive the Selberg trace formula. As an application wedefine the corresponding Selberg zeta-function and compute its divisor, thusgeneralizing results of Elstrodt, Grunewald and Mennicke to non-trivial unitaryrepresentations. We show that the presence of cuspidal elliptic elementssometimes adds ramification point to the zeta function. In fact, if D is thering of Eisenstein integers, then the Selberg zeta-function of PSL(2,D)contains ramification points and is the sixth-root of a meromorphic function.Comment: 25 pages, submitted to Mathematische Zeitschrif

The Selberg trace formula and Selberg zeta-function for cofinite Kleinian groups with finite-dimensional unitary representations