The minimum discriminant of number fields of degree 8 and signature (2,3)

TL;DR

This paper uses algorithmic methods to classify degree 8 number fields with signature (2,3) and bounded discriminant, refining bounds through local corrections and Odlyzko-Poitou-Serre estimates.

Contribution

It provides a complete classification of degree 8 number fields with signature (2,3) below a certain discriminant bound using advanced algorithmic techniques.

Findings

Complete classification of degree 8 fields with discriminant bounds

Refined discriminant bounds using local prime ideal corrections

Application of Hunter and Pohst algorithms for classification

Abstract

In this paper we describe how to use the algorithmic methods provided by Hunter and Pohst in order to give a complete classification of number fields of degree 8 and signature (2,3) with absolute discriminant less than a certain bound. The choice of this bound comes from the local corrections given by prime ideals to the lower estimates for discriminants obtained with the Odlyzko-Poitou-Serre method.