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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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On Selberg's small eigenvalue conjecture and residual eigenvalues

1Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen O, Denmark

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2011, Issue 656, Pages 179–211, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2011.050, March 2011

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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.

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