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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The action of the heat operator on Jacobi forms


Author: Olav K. Richter
Journal: Proc. Amer. Math. Soc. 137 (2009), 869-875
MSC (2000): Primary 11F50; Secondary 11F60
Published electronically: September 15, 2008
MathSciNet review: 2457425
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Abstract: We investigate the action of the heat operator on Jacobi forms. In particular, we present two explicit characterizations of this action on Jacobi forms of index $ 1$. Furthermore, we study congruences and filtrations of Jacobi forms. As an application, we determine when an analog of Atkin's $ U$-operator applied to a Jacobi form is nonzero modulo a prime.


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Additional Information

Olav K. Richter
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: richter@unt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09566-X
PII: S 0002-9939(08)09566-X
Received by editor(s): March 5, 2008
Published electronically: September 15, 2008
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society