1 november 2007, kl 14.00-15.00, Uppsala, Ångström, Häggsalen.

Morten Risager (University of Aarhus): Selberg's eigenvalue conjecture and poles of Eisenstein series

Abstract. Selberg conjectured that the automorphic Laplacian related to a congruence group has no eigenvalues in the open interval ]0,1/4[. We will explain how this important conjecture surprisingly may be reformulated entirely in terms of existence of poles of Eisenstein series for system of Laplacians with characters. This is done using a combination of techniques from perturbation theory and non-vanishing of arithmetic L-functions.