Congruences in Hermitian Jacobi and Hermitian modular forms

Abstract

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 \u2062 ( i ) {\\mathbb{Q}(i)} . We then apply the mod p theory of Hermitian Jacobi forms to characterize U \u2062 ( p ) {U(p)} congruences and to study Ramanujan-type congruences for Hermitian Jacobi forms and Hermitian modular forms of degree 2 over ℚ \u2062 ( i ) {\\mathbb{Q}(i)} .