<i>L</i>-functions for Sp(<i>2n</i>) × GL(<i>k</i>) via Non-unique Models

Abstract Let $n$ and $k$ be positive integers such that $n$ is even. We derive new global integrals for $\textrm{Sp}_{2n}\times \textrm{GL}_{k}$ from the generalized doubling method of Cai, Friedberg, Ginzburg, and Kaplan, following a strategy and extending a previous result of Ginzburg and Soudry on the case $n=k=2$. We show that these new integrals unfold to non-unique models on $\textrm{Sp}_{2n}$. Using the New Way method of Piatetski-Shapiro and Rallis, we show that these new global integrals represent the $L$-functions for $\textrm{Sp}_{2n}\times \textrm{GL}_{k}$, generalizing a previous result of the second-named author on $\textrm{Sp}_{4}\times \textrm{GL}_{2}$ and a previous work of Piatetski-Shapiro and Rallis on $\textrm{Sp}_{2n}\times \textrm{GL}_{1}$.