On the Rankin-Selberg gamma factor of simple supercuspidal representations of the even unitary group for p-adic local fields

Abstract

Let π be a simple supercuspidal representation of the quasi-split unramified even unitary group with respect to an unramified quadratic extension $E/F$ of p-adic fields. We compute the Rankin-Selberg gamma factor for rank-1 twists of π by a tamely ramified character of $E^{\times }$. For non-dyadic cases, the gamma factor can also be derived from the fact that endoscopic lift is also simple supercuspidal. For the dyadic case, the result is original. We expect to extend the result on the endoscopic lift to the dyadic case with our computation.