On Selberg's small eigenvalue conjecture and residual eigenvalues

TY - JOUR

T1 - On Selberg's small eigenvalue conjecture and residual eigenvalues

AU - Risager, Morten S.

PY - 2011/7

Y1 - 2011/7

N2 - 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.

AB - 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.

M3 - Journal article

SN - 0075-4102

VL - 656

SP - 179

EP - 211

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

ER -