Determination of Hilbert modular forms using squarefree coefficients
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.
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