Euclidean minima of algebraic number fields

TL;DR

This paper improves the upper bounds on the Euclidean minima of algebraic number fields by leveraging previous results and considering factors like degree, signature, discriminant, and Hermite constant.

Contribution

It introduces a refined upper bound for Euclidean minima that depends on multiple invariants of algebraic number fields, extending prior work.

Findings

New upper bound depending on degree, signature, discriminant, and Hermite constant

Enhanced understanding of Euclidean minima in algebraic number fields

Application of previous results to improve bounds

Abstract

In this paper, we use some of our previous results to improve an upper bound of Bayer-Fluckiger, Borello and Jossen on the Euclidean minima of algebraic number fields. Our bound depends on the degree $n$ of the field, its signature, discriminant and the Hermite constant in dimension $n$.