Joint IAS/Princeton University Number Theory Seminar

The Arthur-Selberg trace formula is a powerful tool in the theory of automorphic forms. Roughly speaking, it expresses the character of the regular representation on the automorphic spectrum in terms of distributions indexed by conjugacy classes. The terms attached to elliptic (resp. hyperbolic) regular semi-simple conjugacy classes are the global ordinary (resp. weighted) orbital integrals. The contributions of the other conjugacy classes are not so explicit. In the talk, I will explain that some unipotent contributions can also be expressed as global unipotent weighted orbital integrals. Some others are "regularized" orbital integrals. If time permits, I will discuss some conjectures and motivations.