Stability of Rankin–Selberg gamma factors for Sp(2n),Sp̃(2n) and U(n,n)

Abstract

Let [Formula: see text] be a [Formula: see text]-adic field and [Formula: see text] be a quadratic extension. In this paper, we prove a stability result on partial Bessel functions associated with Howe vectors for generic representations of reductive group of type [Formula: see text]. As a consequence, we reprove the stability of Rankin–Selberg gamma factors for [Formula: see text] and [Formula: see text] when the characteristic of the residue field of [Formula: see text] is not [Formula: see text].