Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms
Number Theory
2012-02-02 v1
Abstract
We give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on GL(2) over Q. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. We include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, we 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.
Cite
@article{arxiv.1202.0189,
title = {Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms},
author = {Charles Li and Andrew Knightly},
journal= {arXiv preprint arXiv:1202.0189},
year = {2012}
}
Comments
145 pages. To appear in Mem. Amer. Math. Soc