Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms (Memoirs of the American Mathematical Society) by A. Knightly
English | 2013 | ISBN: 0821887440 | 132 Pages | PDF | 1.30 MB
English | 2013 | ISBN: 0821887440 | 132 Pages | PDF | 1.30 MB
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.