Binary normal regular Hermitian lattices over imaginary quadratic fields

TL;DR

This paper classifies binary regular Hermitian lattices over imaginary quadratic fields, providing a complete list of such lattices and analyzing their properties in relation to local representability of integers.

Contribution

It offers the first comprehensive classification of binary regular Hermitian lattices over imaginary quadratic fields, expanding understanding of their structure and representation properties.

Findings

Complete list of binary regular Hermitian lattices over imaginary quadratic fields

Characterization of local representability of integers by these lattices

Insights into the structure and regularity conditions of Hermitian lattices

Abstract

We call a positive definite Hermitian lattice regular if it represents all integers which can be represented locally by the lattice. We investigate binary regular Hermitian lattices over imaginary quadratic fields $\mathbb{Q}(\sqrt{-m})$ and provide a complete list of the (normal) Hermitian lattices.