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Determination of Hilbert modular forms using squarefree coefficients (2403.16012v2)
Published 24 Mar 2024 in math.NT
Abstract: Let $F$ (over $\mathbb{Q}$) 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.