Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. R. Berndt, Zur Arithmetik der elliptischen Funktionenkörper höherer Stufe, J. Reine Angew. Math. 326 (1981), 79-94 MR 84h:10029a
  • 2. R.E. Borcherds, Automorphic forms on $O_{s+2,2}({\mathbf R})$ and infinite products, Invent. Math. 120 (1995), 161-213 MR 96j:11067
  • 3. 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.
  • 4. W. Eholzer and N.-P. Skoruppa, Product expansions of conformal characters, Phys. Lett. B 388 (1996), 82-89 MR 97k:81132
  • 5. M. Eichler and D. Zagier, The theory of Jacobi forms, Progress in Math. vol. 55, Birkhäuser: Boston 1985 MR 86j:11043
  • 6. B. Gross and D. Zagier, Heegner points and derivatives of $L$-series, Invent. Math. 84 (1986), 225-320 MR 87j:11057
  • 7. B. Gross and D. Zagier, On singular moduli, J. reine Angew. Math. 355 (1985), 191-220 MR 86j:11041
  • 8. N. Katz, $p$-adic properties of modular schemes and modular forms. In: Modular Functions of One Variable III (eds.: W. Kuyk and J.-P. Serre), pp. 69-122, LNM 350, Springer: Berlin Heidelberg New York, 1973 MR 56:5434
  • 9. S. Lang, Elliptic functions, Addison-Wesley: London 1973 MR 53:13117
  • 10. D. Zagier, Traces of singular moduli, preprint 2000

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F03, 11G05

Retrieve articles in all journals with MSC (2000): 11F03, 11G05

Additional Information

YoungJu Choie
Affiliation: Department of Mathematics, Pohang Institute of Science and Technology, Pohang 790-784, Korea

Winfried Kohnen
Affiliation: Mathematisches Institut, Universität Heidelberg, INF 288, D-69120 Heidelberg, Germany

Received by editor(s): May 24, 2002
Published electronically: February 14, 2003
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society