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Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families

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Author(s)
Kim, Ju-Lee
•
Shin, Sug Woo
•
Templier, Nicolas
Date Issued
2020
Journal
Advances in Mathematics
Publisher
Elsevier BV
Version
Final published version
Abstract
© 2019 The Authors We establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes. For the tame supercuspidals constructed by J.-K. Yu we prove the limit multiplicity property with error terms. Thereby we obtain a Sato-Tate equidistribution for the Hecke eigenvalues of these families. The main new ingredient is to show that the orbital integrals of matrix coefficients of tame supercuspidal representations with increasing formal degree on a connected reductive p-adic group tend to zero uniformly for every noncentral semisimple element.
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DOI of Published Version
10.1016/J.AIM.2019.106955
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