On Rankin–Cohen brackets of Jacobi forms and Jacobi Poincaré series of matrix index

Abstract

We prove that if a Rankin–Cohen bracket of two complex valued functions f and g on H×C(g×1) is a Jacobi form and if f is a Jacobi form and g has certain type of Fourier expansion, then g is also a Jacobi form. We also prove a relation between Rankin–Cohen brackets of certain Jacobi forms and Jacobi Poincaré series. © The Indian National Science Academy 2024.