English

The Weyl law for algebraic tori

Number Theory 2024-02-29 v3 Representation Theory

Abstract

We give an asymptotic evaluation for the number of automorphic characters of an algebraic torus TT 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 LL-group of TT. Our results therefore fit into a general framework of counting automorphic representations on reductive groups by analytic conductor.

Keywords

Cite

@article{arxiv.1808.09991,
  title  = {The Weyl law for algebraic tori},
  author = {Ian Petrow},
  journal= {arXiv preprint arXiv:1808.09991},
  year   = {2024}
}

Comments

Final version. To appear in J. Eur. Math. Soc. (JEMS)