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

HTML articles powered by AMS MathViewer

- by YoungJu Choie and Winfried Kohnen
- Proc. Amer. Math. Soc.
**131**(2003), 3309-3317 - DOI: https://doi.org/10.1090/S0002-9939-03-06945-4
- Published electronically: February 14, 2003
- PDF | Request permission

## 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 $z=0$.## References

- Rolf Berndt,
*Zur Arithmetik der elliptischen Funktionenkörper höherer Stufe*, J. Reine Angew. Math.**326**(1981), 79–94 (German). MR**622346**, DOI 10.1515/crll.1981.326.79 - Richard E. Borcherds,
*Automorphic forms on $\textrm {O}_{s+2,2}(\textbf {R})$ and infinite products*, Invent. Math.**120**(1995), no. 1, 161–213. MR**1323986**, DOI 10.1007/BF01241126 - J.H. Bruinier, W. Kohnen and K. Ono, The arithmetic of the values of modular functions and the divisors of modular forms, to appear in Compos. Math.
- Wolfgang Eholzer and Nils-Peter Skoruppa,
*Product expansions of conformal characters*, Phys. Lett. B**388**(1996), no. 1, 82–89. MR**1418608**, DOI 10.1016/0370-2693(96)01154-9 - Martin Eichler and Don Zagier,
*The theory of Jacobi forms*, Progress in Mathematics, vol. 55, Birkhäuser Boston, Inc., Boston, MA, 1985. MR**781735**, DOI 10.1007/978-1-4684-9162-3 - Benedict H. Gross and Don B. Zagier,
*Heegner points and derivatives of $L$-series*, Invent. Math.**84**(1986), no. 2, 225–320. MR**833192**, DOI 10.1007/BF01388809 - Benedict H. Gross and Don B. Zagier,
*On singular moduli*, J. Reine Angew. Math.**355**(1985), 191–220. MR**772491** - Nicholas M. Katz,
*$p$-adic properties of modular schemes and modular forms*, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973, pp. 69–190. MR**0447119** - Serge Lang,
*Elliptic functions*, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Amsterdam, 1973. With an appendix by J. Tate. MR**0409362** - D. Zagier, Traces of singular moduli, preprint 2000

## Bibliographic 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
- Received by editor(s): May 24, 2002
- Published electronically: February 14, 2003
- Communicated by: David E. Rohrlich
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 3309-3317 - MSC (2000): Primary 11F03, 11G05
- DOI: https://doi.org/10.1090/S0002-9939-03-06945-4
- MathSciNet review: 1990618