Rankin–Cohen brackets of Jacobi forms and Jacobi Poincaré series
Volume 212 / 2024
Acta Arithmetica 212 (2024), 115-132
MSC: Primary 11F50; Secondary 11F60
DOI: 10.4064/aa230117-23-9
Published online: 11 January 2024
Abstract
We prove that if a Rankin–Cohen bracket of a Jacobi form $\phi $ and a complex-valued holomorphic function $\psi $ defined on $\mathcal H\times \mathbb C$ is a Jacobi form, then $\psi $ is a Jacobi form. We also study the relation between Rankin–Cohen brackets of Jacobi forms and Jacobi Poincaré series.
