Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms / A. Knightly, C. Li.

Format:

Book

Author/Creator:

Knightly, Andrew, 1972- author.

Li, C., 1973- author.

Series:

Memoirs of the American Mathematical Society ; Volume 224, Number 1055.

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 224, Number 1055

Language:

English

Subjects (All):

Hecke operators.

Trace formulas.

Physical Description:

1 online resource (132 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

Language Note:

English

Summary:

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.

Contents:

""9.1. A bound for twisted Kloosterman sums""""9.2. Factorization""; ""9.3. Proof of Theorem 9.2""; ""Chapter 10. Equidistribution of Hecke eigenvalues""; ""Bibliography""; ""Notation index""; ""Subject index""

Notes:

"Volume 224, Number 1055 (fourth of 4 numbers)."

Includes bibliographical references and indexes.

Description based on print version record.

ISBN:

1-4704-1006-0