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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
Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms
eBook 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
Add to cart
Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms
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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
eBook 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
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 224; 2013; 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.
  • Table of Contents
     
     
    • 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 publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 224; 2013; 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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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