
Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms
American Mathematical Society (Publisher)
Published on 1. July 2013
Book
Paperback/Softback
132 pages
978-0-8218-8744-8 (ISBN)
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Description
The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
ISBN-13
978-0-8218-8744-8 (9780821887448)
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Schweitzer Classification
Persons
A. Knightly, University of Maine, Orono, ME, USA
C. Li, The Chinese University of Hong Kong, China
C. Li, The Chinese University of Hong Kong, China
Content
Introduction Preliminaries
Bi-$K_\infty$-invariant functions on $\operatorname{GL}_2(\mathbf{R})$
Maass cusp forms
Eisenstein series
The kernel of $R(f)$
A Fourier trace formula for $\operatorname{GL}(2)$
Validity of the KTF for a broader class of $h$ Kloosterman sums
Equidistribution of Hecke eigenvalues
Bibliography
Notation index
Subject index
Bi-$K_\infty$-invariant functions on $\operatorname{GL}_2(\mathbf{R})$
Maass cusp forms
Eisenstein series
The kernel of $R(f)$
A Fourier trace formula for $\operatorname{GL}(2)$
Validity of the KTF for a broader class of $h$ Kloosterman sums
Equidistribution of Hecke eigenvalues
Bibliography
Notation index
Subject index