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

2025/07/22 by Washburn, Sidney · 1 citation
#11F30 (Primary) 11F50 (Secondary) #11F46 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.17002

Abstract

We prove that vector-valued Siegel cusp forms for Γ₀ⁿ(N) with certain nebentypus are determined by their fundamental Fourier coefficients with discriminants coprime to the level N, assuming N is odd and square-free. In the case of genus 3, we strengthen this to Fourier coefficients corresponding to maximal orders in quaternion algebras. We also prove that Jacobi forms of fundamental index with discriminant coprime to the odd level N are determined by their primitive theta components.

Citations

• New bounds for fundamental Fourier coefficients of Siegel modular forms
• Non-vanishing of theta components of Jacobi forms with level and an application
• P-Adic families of Siegel modular cuspforms
• Siegel cusp forms of degree 2 are determined by their fundamental Fourier coefficients
• Siegel cusp forms of degree 2 are determined by their fundamental Fourier coefficients

Cited by

• Fundamental Fourier coefficients of Siegel modular forms of higher degrees and levels

Related

• Siegel cusp forms of degree 2 are determined by their fundamental Fourier coefficients
• Fundamental Fourier coefficients of Siegel modular forms of higher degrees and levels
• On sign changes of primitive Fourier coefficients of Siegel cusp forms
• Non-vanishing of theta components of Jacobi forms with level and an application
• On Fourier coefficients and Hecke eigenvalues of Siegel cusp forms of degree 2