# Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms (Memoirs of the American Mathematical Society 224, 1055)

By: Andrew Knightly (author), C. K. Li (author)Paperback

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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.

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A. Knightly , University of Maine, Orono, ME, USA C. Li , The Chinese University of Hong Kong, China

### Contents

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

### Product Details

• publication date: 30/08/2013
• ISBN13: 9780821887448
• Format: Paperback
• Number Of Pages: 132
• ID: 9780821887448
• ISBN10: 0821887440

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