New bounds for fundamental Fourier coefficients of Siegel modular forms

TL;DR

This paper establishes new bounds for the Fourier coefficients of Siegel modular forms by leveraging Jacobi forms and Iwaniec's method, leading to improved estimates for fundamental coefficients.

Contribution

It introduces novel bounds for Fourier coefficients of Jacobi forms and applies them to degree two Siegel modular forms, enhancing previous estimates.

Findings

New bounds for Jacobi form Fourier coefficients

Strong bounds on fundamental Fourier coefficients of Siegel modular forms

Improved estimates compared to previous results

Abstract

We prove new bounds for the Fourier coefficients of Jacobi forms using a method of Iwaniec. In view of the Fourier-Jacobi expansion of degree two Siegel modular forms, we can use these to obtain strong bounds on fundamental Fourier coefficients of Siegel modular forms.