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Licensed Unlicensed Requires Authentication Published by De Gruyter March 15, 2011

On Selberg's small eigenvalue conjecture and residual eigenvalues

  • Morten S. Risager EMAIL logo


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.

Received: 2007-10-18
Revised: 2010-05-03
Published Online: 2011-03-15
Published in Print: 2011-July

© Walter de Gruyter Berlin · New York 2011

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