An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
Kuznetsov’s Trace Formula and the Hecke Eigenvalues of Maass Forms

A. Knightly University of Maine, Orono, ME
C. Li The Chinese University of Hong Kong, China
Available Formats:
Electronic ISBN: 978-1-4704-1006-3
Product Code: MEMO/224/1055.E
List Price: $73.00 MAA Member Price:$65.70
AMS Member Price: $58.40 Click above image for expanded view Kuznetsov’s Trace Formula and the Hecke Eigenvalues of Maass Forms A. Knightly University of Maine, Orono, ME C. Li The Chinese University of Hong Kong, China Available Formats:  Electronic ISBN: 978-1-4704-1006-3 Product Code: MEMO/224/1055.E  List Price:$73.00 MAA Member Price: $65.70 AMS Member Price:$58.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 2242013; 132 pp
MSC: Primary 11; 22;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Bi-$K_\infty$-invariant functions on $\operatorname {GL}_2(\mathbf {R})$
• 4. Maass cusp forms
• 5. Eisenstein series
• 6. The kernel of $R(f)$
• 7. A Fourier trace formula for $\operatorname {GL}(2)$
• 8. Validity of the KTF for a broader class of $h$
• 9. Kloosterman sums
• 10. Equidistribution of Hecke eigenvalues
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2242013; 132 pp
MSC: Primary 11; 22;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Bi-$K_\infty$-invariant functions on $\operatorname {GL}_2(\mathbf {R})$
• 4. Maass cusp forms
• 5. Eisenstein series
• 6. The kernel of $R(f)$
• 7. A Fourier trace formula for $\operatorname {GL}(2)$
• 8. Validity of the KTF for a broader class of $h$
• 9. Kloosterman sums
• 10. Equidistribution of Hecke eigenvalues
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.