%0 Journal Article
%T On Selberg's small eigenvalue conjecture and residual eigenvalues
%A Morten S. Risager
%J Mathematics
%D 2007
%I arXiv
%X 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.
%U http://arxiv.org/abs/0707.2332v3