We prove an equality between the gamma factors for the Asai cube representation of ${ \rm R}_{ E/F}{ \rm GL}_2$ defined by the Weil$-$Deligne representations and the local zeta integrals of Ikeda and Piatetski-Shapiro$-$Rallis, where $E$ is an \'etale cubic algebra over a local field $F$ of characteristic zero. As an application we obtain the analytic properties of the automorphic $L$-functions for the Asai cube representation.
Categories: math.NT