Note on Hermitian Jacobi Forms

الأصل · EN

We compare the spaces of Hermitian Jacobi forms (HJF) of weight k and indices 1,2 with classical Jacobi forms (JF) of weight k and indices 1,2,4. Using the embedding into JF, upper bounds for the order of vanishing of HJF at the origin is obtained. We compute the rank of HJF as a module over elliptic modular forms and prove the algebraic independence of the generators in case of index 1. Some related questions are discussed.