Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces

Details 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

2003-10-22

arxiv.org/abs/math/0310364v2

Mathematics

Differential Geometry

AMS-LaTeX, 27 pages, 3 figures. Revision adds references and corrects typos

Scientific paper

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.

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