Multiplicity one for certain paramodular forms of genus two

TL;DR

The paper proves a multiplicity one theorem for certain paramodular cuspidal automorphic representations of GSp(4), assuming a hypothesis on non-vanishing of automorphic L-series central values, advancing understanding of automorphic forms.

Contribution

It establishes a multiplicity one result for non-CAP paramodular automorphic representations of GSp(4) under a non-vanishing hypothesis, linking automorphic L-series properties to representation theory.

Findings

Proves multiplicity one for certain paramodular forms of genus two.

Shows these forms are globally generic under specified conditions.

Relies on a hypothesis about non-vanishing of automorphic L-series.

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.