On gamma factors of generic representations of ${\rm U}_{2n+1}\times{\rm Res}_{E/F}{\rm GL}_r$

Abstract: In this article we prove that the gamma factors attached to generic representations of ${\rm U}{2n+1}\times{\rm Res}{E/F}{\rm GL}_r$ over a local field $F$ defined by various approaches coincide when $F$ is non-archimedean and under additional assumptions on $n,r$ and $E$ when $F$ is archimedean.