Asymptotics of automorphic spectra and the trace formula

This paper is a survey article on the limiting behavior of the discrete spectrum of the right regular representation in $L^2(Γ\bs G)$ for a lattice $Γ$ in a reductive group $G$ over a number field. We discuss various aspects of the Weyl law, the limit multiplicity problem, the analytic torsion, and applications to the cohomology of arithmetic groups.

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