Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces
Differential Geometry
2007-05-23 v2 Spectral Theory
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,R) is determined by its trace spectrum up to finitely many possibilities, thus generalizing results of McKean and Mueller to groups which are not necessarily cofinite.
Keywords
Cite
@article{arxiv.math/0310364,
title = {Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces},
author = {D. Borthwick and C. Judge and P. A. Perry},
journal= {arXiv preprint arXiv:math/0310364},
year = {2007}
}
Comments
AMS-LaTeX, 27 pages, 3 figures. Revision adds references and corrects typos