A Multi-variable Rankin-Selberg Integral for a Product of $G{L}_2$-twisted Spinor $L$-functions

Abstract

We consider a new integral representation for $L(s_1,\Pi \times {\tau }_1)L(s_2,\Pi \times {\tau }_2),$ where $\Pi$ is a globally generic cuspidal representation of $GS{p}_4,$ and ${\tau }_1$ and ${\tau }_2$ are two cuspidal representations of $G{L}_2$ having the same central character. As and application, we find a new period condition for two such $L$ functions to have a pole simultaneously. This points to an intriguing connection between a Fourier coefficient of a residual representation on $GSO(12)$ and a theta function on $\widetilde{Sp}(16).$ A similar integral on $GSO(18)$ fails to unfold completely, but in a way that provides further evidence of a connection.

48 pages

References in corpus (1)

• A Cuspidality Criterion for the Exterior Square Transfer of Cusp Forms on GL(4)