GROUP ACTIONS AND AUTOMORPHIC FORMS SEMINAR

2/22/2005

Akshay Venkatesh,
CIMS/CLAY Institute

Existence and Weyl's law for cusp forms

I will explain joint work with Elon Lindenstrauss, establishing Weyl's law for cusp forms on congruence quotients of higher rank symmetric spaces. The key ingredient is a new type of "simple trace formula", which allows us to evade the usual difficulties with Eisenstein series. I will first explain the underlying ideas in the context of the modular surface SL(2,Z)\H, and then discuss how they extend to higher rank quotients.