  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.
