Petrow, Ian;
(2024)
The Weyl law for algebraic tori.
Journal of the European Mathematical Society
, 2024
10.4171/jems/1465.
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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.
| Type: | Article |
|---|---|
| Title: | The Weyl law for algebraic tori |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/jems/1465 |
| Publisher version: | http://dx.doi.org/10.4171/jems/1465 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Weyl law, analytic conductor, automorphic forms, algebraic tori, local Langlands correspondence, Brascamp–Lieb inequality, polymatroid intersection theorem |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10191668 |
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