Doubling zeta integrals and local factors for metaplectic groups

Abstract

We develop the theory of the doubling zeta integral of Piatetski-Shapiro and Rallis for metaplectic groups ${Mp}_{2n}$, and we use it to give precise definitions of the local $\gamma$-factors, $L$-factors, and $ϵ$-factors for irreducible representations of ${Mp}_{2n}\times {GL}_1$, following the footsteps of Lapid and Rallis.