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arXiv · 0707.2332

On Selberg's small eigenvalue conjecture and residual eigenvalues

Morten S. Risager
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Abstract

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.

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Morten S. Risager. 2008-11-07. On Selberg's small eigenvalue conjecture and residual eigenvalues. https://arxiv.org/abs/0707.2332

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