  We develop a reciprocity formula for a spectral sum over central values of
L-functions on GL(4)xGL(2). As an application we show that for any self-dual
cusp form Pi for SL(4,Z), there exists a Maass form pi for SL(2,Z) such that
L(1/2, Pi x pi) is nonvanishing. An important ingredient is a "balanced"
Voronoi summation formula involving Kloosterman sums on both sides, which can
also be thought of as the functional equation of a certain double Dirichlet
series involving Kloosterman sums and GL(4) Hecke eigenvalues.
