The Ramanujan Journal

, Volume 41, Issue 1–3, pp 319–322 | Cite as

Transcendence of zeros of Jacobi forms

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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.

Keywords

Jacobi forms Zeros Transcendency 

Mathematics Subject Classification

Primary 11F50 Secondary 11J81 

Notes

Acknowledgments

The authors thank the referee for useful comments.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsPohang Institute of Science and Technology, POSTECHPohangKorea
  2. 2.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany

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