Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T17:11:26.274Z Has data issue: false hasContentIssue false
  • English
  • Français

HEAT OPERATORS AND QUASIMODULAR FORMS

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  28 January 2010

MIN HO LEE
MIN HO LEE*
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, USA (email: 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 introduce a differential operator on quasimodular polynomials that corresponds to the derivative operator on quasimodular forms. We then prove that such a differential operator is compatible with a heat operator on Jacobi-like forms in certain cases. These results show in those cases that the derivative operator on quasimodular forms corresponds to a heat operator on Jacobi-like forms.

Keywords

quasimodular formsmodular formsheat operatorsJacobi-like forms

MSC classification

Secondary: 11F11: Holomorphic modular forms of integral weight
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 3 , June 2010 , pp. 514 - 522
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Choie, Y. and Lee, M. H., ‘Quasimodular forms, Jacobi-like forms, and pseudodifferential operators’, Preprint.Google Scholar
[2]Cohen, P. B., Manin, Y. and Zagier, D., ‘Automorphic pseudodifferential operators’, in: Algebraic Aspects of Nonlinear Systems (Birkhäuser, Boston, 1997), pp. 17–47.Google Scholar
[3]Eichler, M. and Zagier, D., The Theory of Jacobi Forms, Progress in Mathematics, Vol. 55 (Birkhäuser, Boston, 1985).Google Scholar
[4]Kaneko, M. and Zagier, D., A Generalized Jacobi Theta Function and Quasimodular Forms, Progress in Mathematics, Vol. 129 (Birkhäuser, Boston, 1995), pp. 165–172.Google Scholar
[5]Lee, M. H., ‘Radial heat operators on Jacobi-like forms’, Math. J. Okayama Univ. 104 (2009), 27–46.Google Scholar
[6]Zagier, D., ‘Modular forms and differential operators’, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 57–75.CrossRefGoogle Scholar