Multiplicity one for certain paramodular forms of genus two

Abstract

We show that certain paramodular cuspidal automorphic irreducible representations of $\mathrm{GSp}(4,{\mathbb{A}}_{\mathbb{Q}})$, which are not CAP, are globally generic. This implies a multiplicity one theorem for paramodular cuspidal automorphic representations. Our proof relies on a reasonable hypothesis concerning the non-vanishing of central values of automorphic $L$-series.

10 pages