On the Rankin-Selberg integral of Kohnen and Skoruppa

The Rankin-Selberg integral of Kohnen and Skoruppa produces the Spin $L$-function for holomorphic Siegel modular forms of genus two. In this paper, we reinterpret and extend their integral to apply to arbitrary cuspidal automorphic representations of ${\mathrm{P}\mathrm{G}\mathrm{S}\mathrm{p}}_4$. We show that the integral is related to a non-unique model and analyze it using the approach of Piatetski-Shapiro and Rallis.