The action of the heat operator on Jacobi forms

Richter, Olav

doi:10.1090/S0002-9939-08-09566-X

The action of the heat operator on Jacobi forms
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by Olav K. Richter PDF

Proc. Amer. Math. Soc. 137 (2009), 869-875 Request permission

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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