New bounds for fundamental Fourier coefficients of Siegel modular forms

2024/11/01 by Edgar Assing, Assing, Edgar · 1 citation
Mathematics · #11F30 #11F46 #11F50 #11L05 #Advanced Algebra and Geometry #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2411.00450

openalex publication_date 2024/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Certain Siegel Cusp Forms with Level are Determined by their Fundamental Fourier Coefficients

Related

• Improved bounds for Fourier coefficients of Siegel modular forms
• On Fourier coefficients of elliptic modular forms \bmod ℓ with applications to Siegel modular forms
• Some relations on Fourier coefficients of degree 2 Siegel forms of\n arbitrary level
• Fundamental Fourier coefficients of Siegel modular forms of higher degrees and levels
• Sturm Bounds for Siegel Modular Forms