# Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms

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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.AMS Author Handbook and the Instruction Manual are available in PDF format from the author package link. ... CD to the Electronic Prepress Department, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA.

 Title : Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms Author : Andrew Knightly, C. Li Publisher : American Mathematical Soc. - 2013-06-28