The Weyl law for algebraic tori

2018/08/29 by Petrow, Ian · 1 citation
#11F55 11F66 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1808.09991

Abstract

We give an asymptotic evaluation for the number of automorphic characters of an algebraic torus T with bounded analytic conductor. The analytic conductor which we use 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.

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