Families of Cyclic Cubic Fields

TL;DR

This paper presents a method for generating families of cyclic cubic fields with explicit fundamental units, encompassing all known families and introducing new ones, advancing the understanding of their structure.

Contribution

It introduces a comprehensive procedure that generates all known and new families of cyclic cubic fields with explicit fundamental units.

Findings

All known families are generated by the method.

New families of cyclic cubic fields are constructed.

The method provides explicit fundamental units for these fields.

Abstract

We describe a procedure for generating families of cyclic cubic fields with explicit fundamental units. This method generates all known families and gives new ones.