Whittaker functions for generalized principal series representations of GSp(2,R)

Abstract

We study Whittaker functions for generalized principal series representations of GSp(2,R) induced from Siegel parabolic subgroup. We give Mellin–Barnes type integral representations of Whittaker functions belonging to certain K-types. As an application of our explicit formulas, we compute the archimedean parts of Novodvorsky's zeta integrals. As a consequence we can show the entireness of the spinor L-functions for generic cusp forms on GSp(2).