Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms

著者

• Knightly, Andrew
• Li, C.

書誌事項

Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms

A. Knightly, C. Li

（Memoirs of the American Mathematical Society, no. 1055）

American Mathematical Society, c2012

注記

"July 2013, volume 224, number 1055 (fourth of 4 numbers)."

Includes bibliographical references (p. 125-128) and indexes

内容説明・目次

内容説明

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.

目次

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

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詳細情報

• NII書誌ID(NCID): BB13017062
• ISBN:
  • 9780821887448
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: v, 132 p.
• 大きさ: 26 cm
• 親書誌ID:
  • BA00035927