The Weyl law for algebraic tori

Abstract

We give an asymptotic evaluation for the number of automorphic characters of an algebraic torus $T$ with bounded analytic conductor. The analytic conductor is defined via the local Langlands correspondence for tori by choosing a finite-dimensional complex algebraic representation of the $L$-group of $T$. Our results therefore fit into a general framework of counting automorphic representations on reductive groups by analytic conductor.