Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces
Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces
For hyperbolic Riemann surfaces of finite geometry, we study Selberg's zeta function and its relation to the relative scattering phase and the resonances of the Laplacian. As an application we show that the conjugacy class of a finitely generated, torsion-free, discrete subgroup of \operatorname{SL}(2,{\mathbb R}) is determined by its trace …