Rankin–Cohen brackets of Jacobi forms and Jacobi Poincaré series

Abstract

We prove that if a Rankin–Cohen bracket of a Jacobi form ϕ and a complex-valued holomorphic function ψ defined on H × C is a Jacobi form, then ψ is a Jacobi form. We also study the relation between Rankin–Cohen brackets of Jacobi forms and Jacobi Poincaré series. © Instytut Matematyczny PAN, 2024.