Non-vanishing of fundamental Fourier coefficients of paramodular forms

TL;DR

This paper proves that paramodular newforms of odd square-free level possess infinitely many non-zero fundamental Fourier coefficients, advancing understanding of their Fourier expansion properties.

Contribution

It establishes the non-vanishing of fundamental Fourier coefficients for a broad class of paramodular newforms, a previously unresolved problem.

Findings

Infinitely many non-zero fundamental Fourier coefficients for these forms

Extension of non-vanishing results to paramodular forms of odd square-free level

New techniques for analyzing Fourier coefficients of paramodular forms

Abstract

We prove that paramodular newforms of odd square-free level have infinitely many non-zero fundamental Fourier coefficients.