Hermitian Jacobi forms and $U(p)$ congruences

Abstract

We introduce a new space of Hermitian Jacobi forms, and we determine its structure. Moreover, we characterize U (p) congruences of Hermitian Jacobi forms, and we discuss an explicit example.

Congruences in Hermitian Jacobi and Hermitian modular forms

“…In the following theorem we give a characterization of U (p) congruences for Hermitian Jacobi forms in terms of filtrations. The following result generalizes the result of Richter and Senadheera [25,Theorem 1.2] to Hermitian Jacobi forms of any integer index.…”

“…Our next result is the main result of this subsection. by Richter and Senadheera [25] and Senadheera [26]. We also explain how one gets more examples of Hermitian Jacobi forms of index > 1 from Hermitian Jacobi forms of index 1.…”

“…On the other hand, Ramanujan-type congruences for Jacobi forms and Siegel modular forms of degree 2 were studied by Dewar and Richter [7] using the theories of Jacobi forms mod p and Siegel modular forms of degree 2 mod p. In this paper we study U (p) congruences and Ramanujan-type congruences for Hermitian Jacobi forms and Hermitian modular forms of degree 2 over Q(i). To study these results, one needs to know the theories of Hermitian Jacobi forms modulo p and Hermitian modular forms modulo p. The theory of Hermitian Jacobi forms mod p has been studied by Richter and Senadheera [25]. But they have studied only Hermitian Jacobi forms of index 1.…”