Stability of Rankin-Selberg gamma factors for $\textrm{Sp}(2n)$, $\widetilde{ \textrm{Sp}}(2n)$ and $\textrm{U}(n,n)$

Abstract

Let $F$ be a $p$-adic field and $E/F$ be a quadratic extension. In this paper, we prove the stability of Rankin-Selberg gamma factors for $\textrm{Sp}_{2n}(F)$, $\widetilde {\textrm{Sp}}_{2n}(F)$ and $\textrm{U}_{E/F}(n,n)$ when the characteristic of the residue field of $F$ is not $2$.