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

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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About Author

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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