Transcendence of zeros of Jacobi forms |
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Authors: | YoungJu Choie Winfried Kohnen |
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Institution: | 1.Department of Mathematics,Pohang Institute of Science and Technology, POSTECH,Pohang,Korea;2.Mathematisches Institut,Universit?t Heidelberg,Heidelberg,Germany |
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Abstract: | A special case of a fundamental theorem of Schneider asserts that if \(j(\tau )\) is algebraic (where j is the classical modular invariant), then any zero z not in \(\mathbf{Q}.L_\tau := \mathbf{Q}\oplus \mathbf{Q}\tau \) of the Weierstrass function \(\wp (\tau ,\cdot )\) attached to the lattice \(L_\tau =\mathbf{Z}\oplus \mathbf{Z}\tau \) is transcendental. In this note we generalize this result to holomorphic Jacobi forms of weight k and index \(m\in \mathbf{N}\) with algebraic Fourier coefficients. |
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