Simple proofs for universal binary Hermitian lattices

TL;DR

This paper provides simple, unified proofs demonstrating that certain positive definite binary Hermitian lattices are universal, meaning they represent all positive integers, simplifying previous complex proofs.

Contribution

The paper introduces straightforward and unified proofs for the universality of binary Hermitian lattices, replacing more complicated prior methods.

Findings

Identified 25 universal binary Hermitian lattices.

Provided simplified proofs for their universality.

Streamlined the proof process compared to previous ad hoc methods.

Abstract

If a positive definite Hermitian lattice represents all positive integers, we call it universal. Several mathematicians, including the author, found 25 universal binary Hermitian lattices. But their ad hoc proofs are complicated. We give simple and unified proofs.