L-Functions for GSp(2) x GL(2): Archimedean Theory and Applications

Let Pi be a generic cuspidal automorphic representation of GSp(2) defined over a totally real algebraic number field k whose archimedean type is either a (limit of) large discrete series representation or a certain principal series representation. Through explicit computation of archimedean local zeta integrals, we prove the functional equation of tensor product L-functions L(s, Pi x sigma) for an arbitrary cuspidal automorphic representation sigma of GL(2). We also give an application to the spinor L-function of Pi.