Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-15T04:21:46.136Z Has data issue: false hasContentIssue false
  • English
  • Français

Vector-Valued Modular Forms of Weight Two Associated With Jacobi-Like Forms

Published online by Cambridge University Press:  20 November 2018

Min Ho Lee
Min Ho Lee*
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A. e-mail: lee@math.uni.edu
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 construct vector-valued modular forms of weight 2 associated to Jacobi-like forms with respect to a symmetric tensor representation of $\Gamma$ by using the method of Kuga and Shimura as well as the correspondence between Jacobi-like forms and sequences of modular forms. As an application, we obtain vector-valued modular forms determined by theta functions and by pseudodifferential operators.

Keywords

11F1111F50

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 3 , 01 September 2006, pp. 428 - 437
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Cohen, P., Manin, Y., and Zagier, D., Automorphic pseudodifferential operators. In: Algebraic Aspects of Nonlinear Systems, Progr. Nonlinear Differential Equations Appl. 26, Birkhäuser, Boston, 1997, pp. 17–47.Google Scholar
[2] Dong, C. and Mason, G., Transformation laws for theta functions. In: Proceedings onMoonshine and Related Topics, CRM Proc. Lecture Notes 30, American Mathematical Society, Providence, RI, 2001, pp. 15–26.Google Scholar
[3] Eichler, M., Eine Verallgemeinerung der Abelschen Integrals. Math. Z. 67(1957), 267–298.Google Scholar
[4] Eichler, M. and Zagier, D., The Theory of Jacobi Forms, Progress in Mathematics 55, Birkhäuser, Boston, 1985.Google Scholar
[5] Kuga, M. and Shimura, G., On vector differential forms attached to automorphic forms. J. Math. Soc. Japan 12(1960), 258–270.Google Scholar
[6] Lee, M. H., Modular forms associated to theta functions. Canad. Math. Bull. 45(2002), no. 2, 257–264.Google Scholar
[7] Shimura, G., Sur les intégrales attachées aux formes automorphes. J. Math. Soc. Japan 11(1959), 291–311.Google Scholar
[8] Zagier, D., Modular forms and differential operators. Proc. Indian Acad. Sci. Math. Sci. 104(1994), no. 1, 57–75.Google Scholar