EXPLICIT DOUBLING INTEGRALS FOR Sp2(F) AND $\widetilde{{{\rm Sp}}_{2}}(F)$ USING "GOOD TEST VECTORS"
In this paper, we offer some explicit computations of a formulation of the doubling method of Piatetski-Shapiro and Rallis for the groups Sp 2(F) (the rank 2 symplectic group) and its metaplectic cover [Formula: see text] for F a finite extension of ℚp with p ≠ 2. We determine a set of "good test vectors" for the irreducible constituents of unramified principal series representations for these groups as well as a set of "good theta test sections" in a family of degenerate principal series representations of Sp 4(F) and [Formula: see text]. Determining "good test data" that produces a non-vanishing doubling integral should indicate the existence of a non-vanishing theta lifts for dual pairs of the type ( Sp 2(F), O (V)) (respectively [Formula: see text]) where V is a quadratic space of an even (respectively odd) dimension.