On the asymptotics of Hecke operators for reductive groups

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In this paper, we study the asymptotic behavior of the traces of Hecke operators for spherical discrete automorphic representations of fixed level on general split reductive groups over Q. Under a condition on the analytic behavior of intertwining operators, which is known for the classical groups and the exceptional group G2, we obtain the expected asymptotics in terms of the spherical Plancherel measure and an explicit estimate for the remainder.
Original languageEnglish
JournalMathematische Annalen
Volume380
Issue number3-4
Pages (from-to)1037-1104
ISSN0025-5831
DOIs
Publication statusPublished - 2021

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