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

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

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Differential Geometry, Spectral Theory, 58J50

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http://salesiana.dossiersoluciones.com/handle/123456789/68959

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0310364
 http://arxiv.org/abs/math/0310364

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arXiv