Determination of Hilbert modular forms using squarefree coefficients

2024/03/24 by Rishabh Agnihotri, Agnihotri, Rishabh, Krishnarjun Krishnamoorthy +1
Mathematics · #11F27 #11F37 #11F41 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2403.16012

openalex publication_date 2024/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F (over ℚ) be a totally real number field of narrow class number 1. We generalize a result of Kohnen on the determination of half integral weight modular forms by their Fourier coefficients supported on squarefree (algebraic) integers. We also give a soft proof that infinitely many Fourier coefficients supported on squarefree integers are non-vanishing.

Related

• Non-vanishing Fourier coefficients of modular forms
• On Fourier coefficients of modular forms of half integral weight at squarefree integers
• Computing Hilbert modular forms over fields with nontrivial class group
• The Arithmetic of the Fourier Coefficients of Automorphic Forms
• On the Divisibility Properties of the Fourier Coefficients of Meromorphic Hilbert Modular Forms