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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Special values of elliptic functions at points of the divisors of Jacobi forms


Authors: YoungJu Choie and Winfried Kohnen
Journal: Proc. Amer. Math. Soc. 131 (2003), 3309-3317
MSC (2000): Primary 11F03, 11G05
Published electronically: February 14, 2003
MathSciNet review: 1990618
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Abstract: The main result of the paper gives an explicit formula for the sum of the values of even order derivatives with respect to $z$ of the Weierstrass $\wp$-function $\wp(\tau,z)$ for the lattice ${\mathbf Z}\tau\oplus{\mathbf Z}$ (where $\tau$ is in the upper half-plane) extended over the points in the divisor of $\phi(\tau,\cdot)$ (where $\phi(\tau,z)$ is a meromorphic Jacobi form) in terms of the coefficients of the Laurent expansion of $\phi(\tau,z)$ around $z=0$.


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Additional Information

YoungJu Choie
Affiliation: Department of Mathematics, Pohang Institute of Science and Technology, Pohang 790-784, Korea
Email: yjc@postech.ac.kr

Winfried Kohnen
Affiliation: Mathematisches Institut, Universität Heidelberg, INF 288, D-69120 Heidelberg, Germany
Email: winfried@mathi.uni-heidelberg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06945-4
PII: S 0002-9939(03)06945-4
Received by editor(s): May 24, 2002
Published electronically: February 14, 2003
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2003 American Mathematical Society