Abstract
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 $\SL(2,{\mathbb R})$ is determined by its trace spectrum up to finitely many possibilities, thus generalizing results of McKean [20] and Muller [23] to groups which are not necessarily cofinite
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have