Existence and Weyl's law for spherical cusp forms
Elon Lindenstrauss, Akshay Venkatesh
Abstract
Let G be a split adjoint semisimple group over Q and K a maximal compact subgroup of the real points G(R). We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms on congruence quotients of G(R)/K. This proves a conjecture of Sarnak for Q-split groups, previously known only for the case of PGL(n). The key idea amounts to a new type of simple trace formula.
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