2-universal Hermitian lattices over imaginary quadratic fields

TL;DR

This paper classifies all 2-universal Hermitian lattices of ranks three and four over imaginary quadratic fields, expanding understanding of their universality properties in number theory.

Contribution

It provides a complete classification of 2-universal ternary and quaternary Hermitian lattices over imaginary quadratic fields, a previously unresolved problem.

Findings

All 2-universal ternary Hermitian lattices identified.

All 2-universal quaternary Hermitian lattices identified.

The classification covers all imaginary quadratic fields.

Abstract

A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find all 2-universal ternary and quaternary Hermitian lattices over imaginary quadratic number fields.