On Selberg's small eigenvalue conjecture and residual eigenvalues
Number Theory
2008-11-07 v3 Spectral Theory
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.
Cite
@article{arxiv.0707.2332,
title = {On Selberg's small eigenvalue conjecture and residual eigenvalues},
author = {Morten S. Risager},
journal= {arXiv preprint arXiv:0707.2332},
year = {2008}
}
Comments
33pages, Various expository corrections