On Selberg's small eigenvalue conjecture and residual eigenvalues

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We show that Selberg's eigenvalue conjecture concerning small eigenvalues of the automorphic Laplacian for congruence groups is equivalent to a conjecture about the non-existence of residual eigenvalues for a perturbed system. We prove this using a combination of methods from asymptotic perturbation theory and number theory.
33pages, Various expository corrections

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Number Theory, Spectral Theory, 11F72; 11M36

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http://salesiana.dossiersoluciones.com/handle/123456789/173360

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0707.2332
 http://arxiv.org/abs/0707.2332

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arXiv