Jacobi forms that characterize paramodular forms

TL;DR

This paper characterizes paramodular forms through their Fourier Jacobi expansions, identifying conditions on Jacobi coefficients that distinguish them, with evidence suggesting some conditions may be unnecessary.

Contribution

It provides a new characterization of paramodular forms via Fourier Jacobi expansions, including growth and linear relation conditions, supported by theoretical and computational examples.

Findings

Growth condition may be superfluous for characterization

Provides theoretical and computational evidence

Offers a new perspective on paramodular form characterization

Abstract

The Fourier Jacobi expansions of paramodular forms are characterized from among all formal series of Jacobi forms by two conditions on the Fourier coeffcients of the Jacobi forms: a growth condition and a set of linear relations. Examples, both theoretical and computational, indicate that the growth condition may be superfluous.