2006-10-27

Jean-Pierre Labesse, Université d'Aix-Marseille II

A simple form of the trace formula and applications

The Selberg trace formula for arbitrary reductive groups over a number field, due to J. Arthur, is a quite powerful tool but also quite difficult to use. A simple form of it is often enough for various applications, among which we shall discuss two examples:

  1. a weak form of the Weyl law for the asymptotics of the number of eigenvalues of the Laplacian on locally symmetric manifolds;
  2. instances of cyclic base change for automorphic representations.