Differential operators on Jacobi forms of half integral weight

Abstract

There is an analogy of Bol's result for Jacobi forms of half integral weight by using the heat operator, and it was later extended to harmonic Maass-Jacobi forms. In this paper, we study more about the behavior of harmonic Maass-Jacobi forms under the heat operator. As an application, we obtain an identity between the Fourier coefficients of the images of harmonic Maass-Jacobi forms under the heat operator and those of harmonic skew-Maass-Jacobi forms. © 2024 Elsevier Inc.