Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms
Author(s)
Bibliographic Information
Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms
（Memoirs of the American Mathematical Society, no. 1055）
American Mathematical Society, c2012
Available at / 10 libraries
-
No Libraries matched.
- Remove all filters.
Note
"July 2013, volume 224, number 1055 (fourth of 4 numbers)."
Includes bibliographical references (p. 125-128) and indexes
Description and Table of Contents
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.
Table of 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
by "Nielsen BookData"
