Congruences in Hermitian Jacobi and Hermitian modular forms

Abstract

In this paper we first prove an isomorphism between certain spaces of Jacobi forms. Using this isomorphism, we study the mod p theory of Hermitian Jacobi forms over Q(i). We then apply the mod p theory of Hermitian Jacobi forms to characterize U (p) congruences and to study Ramanujan-type congruences for Hermitian Jacobi forms and Hermitian modular forms of degree 2 over Q(i).