Euclid's Algorithm in quartic CM-fields
Franz Lemmermeyer
TL;DR
This paper develops techniques to compute inhomogeneous minima of norm forms and applies them to identify all norm-Euclidean complex bicyclic quartic number fields.
Contribution
It introduces methods for computing inhomogeneous minima and classifies all norm-Euclidean complex bicyclic quartic fields.
Findings
Identified all norm-Euclidean complex bicyclic quartic fields.
Developed techniques for computing inhomogeneous minima.
Enhanced understanding of Euclid's algorithm in quartic CM-fields.
Abstract
In this note we present techniques to compute inhomogeneous minima of norm forms; as an application, we determine all norm-Euclidean complex bicyclic quartic number fields.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Cryptography and Residue Arithmetic