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Existence and Weyl's law for spherical cusp forms

Elon Lindenstrauss·Akshay Venkatesh
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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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BibTeXRIS

Elon Lindenstrauss, Akshay Venkatesh. 2005-03-31. Existence and Weyl's law for spherical cusp forms. https://arxiv.org/abs/math/0503724

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