# Congruences in Hermitian Jacobi and Hermitian modular forms

## TL;DR

This paper establishes an isomorphism between spaces of Hermitian Jacobi forms and explores their mod p properties, including congruences and Ramanujan-type congruences for Hermitian modular forms over it.

## Contribution

It introduces a new isomorphism linking Hermitian Jacobi forms and advances the understanding of their mod p congruences and Ramanujan-type properties.

## Key findings

- Proves an isomorphism between certain Hermitian Jacobi form spaces.
- Characterizes U(p) congruences for Hermitian Jacobi forms.
- Studies Ramanujan-type congruences for 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 $\mathbb{Q}(i)$. 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 $\mathbb{Q}(i)$.