Asymptotics for Hecke eigenvalues of automorphic forms on compact arithmetic quotients

In this paper, we describe the asymptotic distribution of Hecke eigenvalues in the Laplace eigenvalue aspect for certain families of Hecke-Maass forms on compact arithmetic quotients. Instead of relying on the trace formula, which was the primary tool in preceding studies on the subject, we use Four...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 404; p. 108372
Main Authors Ramacher, Pablo, Wakatsuki, Satoshi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 06.08.2022
Subjects
Automorphic forms
Compact arithmetic quotients
Equivariant asymptotics
Hecke eigenvalues
Equivariant asymptotics
Compact arithmetic quotients
Automorphic forms
Hecke eigenvalues
58J40
11F12
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Summary:In this paper, we describe the asymptotic distribution of Hecke eigenvalues in the Laplace eigenvalue aspect for certain families of Hecke-Maass forms on compact arithmetic quotients. Instead of relying on the trace formula, which was the primary tool in preceding studies on the subject, we use Fourier integral operator methods. This allows us to treat not only spherical, but also non-spherical Hecke-Maass forms with corresponding remainder estimates. Our asymptotic formulas are available for arbitrary simple and connected algebraic groups over number fields with cocompact arithmetic subgroups.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2022.108372