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arXiv · 1202.0189

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

Charles Li·Andrew Knightly
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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.

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Charles Li, Andrew Knightly. 2012-02-01. Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms. https://arxiv.org/abs/1202.0189

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