| E 2.304??
Vortrag: Asymptotics of traces of Hecke operators
Abstract: The distribution of spectral parameters in families of automorphic representations has many applications, such as density estimates for exceptional eigenvalues or low-lying zeros in families of L-functions. I want to talk about joint work with T. Finis in which we prove an effective equidistribution result for Satake parameters of spherical automorphic forms on many split reductive groups with growing Laplace eigenvalue. Compared to previously known results for GL(n), we can improve the bounds for the remainder terms. As a special case we also obtain the Weyl law on the associated locally symmetric space together with an upper bound for the remainder.