The wave trace for Riemann surfaces
The Selberg trace formula for a Riemann surface of finite geometry with hyperbolic metric is presented. A surface of finite geometry differs from a finite volume one by the fact that it can have a finite number of funnels. These are of a particularly simple geometry, therefore, modulo some regularization, it is possible to transfer the well-known methods of the finite volume case. As an application a new lower bound for the number of resonances is given.
scientific article; zbMATH DE number 1417605