SPINOR L-FUNCTIONS FOR GENERIC CUSP FORMS ON GSp(2) BELONGING TO LARGE DISCRETE SERIES REPRESENTATIONS

Let G = GSp(2) be the symplectic group with similitude of degree two, which is defined over Q. For a generic cusp form F on the adelized group GA which generates a large discrete series representation at infinity, we show that its spinor Lfunction is continued to an entire function and satisfies the functional equation. 0. Introduction. Let G = GSp(2) be the symplectic group with similitude of degree two, defined over a global field k. Suppose that Π = ⊗vΠv is a generic cuspidal automorphic representation of the adelized group GAk , that is, Π has a non-vanishing global Whittaker model. In the 1970’s, Novodvorsky [N, §1] introduced a zeta integral ZN(s, F ) (F ∈ Π) that represents the spinor L-function L(s,Π) of Π. If F ∈ Π is decomposable in the restricted tensor product Π = ⊗vΠv, then the global Whittaker function WF of F can be written as a product of local Whittaker functions: