An Approach to the Selberg Trace Formula via the Selberg Zeta-Function

The Notes give a direct approach to the Selberg zeta—function for cofinite discrete subgroups of SL (2,#3) acting on the upper half—plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta—function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to...