Well-Rounded Twists of Ideal Lattices from Imaginary Quadratic Fields

TL;DR

This paper studies well-rounded twists of ideal lattices from imaginary quadratic fields, proving existence and providing an algorithm to compute all such twists, advancing lattice theory in number fields.

Contribution

It introduces an explicit algorithm to find all well-rounded twists of ideal lattices in imaginary quadratic fields, demonstrating their guaranteed existence.

Findings

Every ideal lattice has at least one well-rounded twist.

An explicit algorithm for computing all well-rounded twists is provided.

The work advances understanding of lattice structures in algebraic number theory.

Abstract

In this paper, we investigate the properties of well-rounded twists of a given ideal lattice of an imaginary quadratic field $K$. We show that every ideal lattice $I$ of $K$ has at least one well-rounded twist lattice. Moreover, we provide an explicit algorithm to compute all well-rounded twists of $I$.