Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T15:42:08.979Z Has data issue: false hasContentIssue false
  • English
  • Français

Construction of Vector Valued Modular Forms from Jacobi Forms

Published online by Cambridge University Press:  20 November 2018

Jae-Hyun Yang
Jae-Hyun Yang*
Affiliation:
Department of Mathematics Inha University Incheon 402-751, Republic of Korea e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a geometrical construction of the canonical automorphic factor for the Jacobi group and construct new vector valued modular forms from Jacobi forms by differentiating them with respect to toroidal variables and then evaluating at zero.

Keywords

11F3011F55
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 6 , 01 December 1995 , pp. 1329 - 1339
Copyright
Copyright © Canadian Mathematical Society 1995

References

[E-Z] Eichler, M. and Zagier, D., The Theory ofJacobi Forms, Progress in Math. 55, Birkhäuser, Boston, Basel, Stuttgart, 1985.Google Scholar
[K-V] Kashiwara, M. and Vergne, M., On the Segal-Shale-Weil Representations and Harmonic Polynomials,, Invent. Math. 44(1978), 1–47.Google Scholar
[M-N-N] Mumford, D., Nori, M. and Norman, P., Tata Lectures on Theta III, Progr. Math. 97, Birkhâuser, 1991.Google Scholar
[N] Namikawa, Y., Toroidal compactification of Siege I spaces, Springer-Verlag 812, 1980.Google Scholar
[PS] Piateski-Sharpiro, I., Automorphic Functions and the Geometry of Classical Domains, Gordan-Breach, New York, 1966.Google Scholar
[Y1] Yang, J.-H., Harmonic Analysis on the Quotient Spaces ofHeisenberg Groups, Nagoya Math. J. 123(1991), 103-117.Google Scholar
[Y2] Yang, J.-H., Harmonic Analysis on the Quotient Spaces of Heisenberg Groups II, J. Number Theory (1) 49(1994), 63–72.Google Scholar
[Y3] Yang, J.-H., Some Results on Jacobi Forms of Higher Degree, Proc. RIMS Symp. on Automorphic Forms and Associated Zeta Functions, Kyoto 805, 1992. 36-50.Google Scholar
[Y4] Yang, J.-H., The Siegel-Jacobi Operator, Abh. Math. Sem. Univ. Hamburg 63(1993), 135–146.Google Scholar
[Y5] Yang, J.-H., Remarks on Jacobi Forms of Higher Degree, Proc. of the 1993 Workshop on Automorphic Forms and Related Topics, The Pyungsan Institute for Mathematical Sciences, Seoul, 1993. 33—58.Google Scholar
[Y6] Yang, J.-H., Singular Jacobi Forms, Trans. Amer. Math. Soc, 347(1995), 2041.2049.Google Scholar
[Z] Ziegler, C., Jacobi Forms of Higher Degree, Abh. Math. Sem. Univ. Hamburg 59(1989), 191–224.Google Scholar