Journal of the Ramanujan Mathematical Society
Volume 41, Issue 1, March 2026 pp. 41–51.
Differential operators for Hermitian Jacobi forms and Hermitian Jacobi
Poincaré series
Authors:
Mohd Shahvez Alam and Animesh Sarkar
Author institution:Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi 221 005,
Uttar Pradesh, India.
Summary:
Assuming that the Rankin-Cohen bracket of two complex-valued holomorphic functions defined on
H × ℂ{2} is a Hermitian Jacobi form, we prove that both functions have to be Hermitian Jacobi forms, if at least one of
them is. We also study the relation between Rankin-Cohen brackets of Hermitian Jacobi forms and Hermitian Jacobi
Poincaré series. Finally, we construct certain Hermitian Jacobi cusp forms by computing the adjoint of higher-order
heat operator for Hermitian Jacobi forms with respect to the Petersson scalar product.
Contents
Full-Text PDF