#### Filter Results:

#### Publication Year

2005

2013

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

This article deals with the determination of the Euclidean minimum M (K) of a totally real number field K of degree n ≥ 2, using techniques from the geometry of numbers. Our improvements of existing algorithms allow us to compute Euclidean minima for fields of degree 2 to 8 and small discrim-inants, most of which were previously unknown. Tables are given at… (More)

- Jean-Paul Cerri
- 2005

- Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski
- 2013

In this article we study totally definite quaternion fields over the rational field and over quadratic number fields. We establish a complete list of all such fields which are Euclidean. Moreover, we prove that every field in this list is in fact norm-Euclidean. The proofs are both theoretical and algorithmic.

We give examples of Generalized Euclidean but not norm-Euclidean number fields of degree greater than 2. In the same way we give examples of 2-stage Euclidean but not norm-Euclidean number fields of degree greater than 2. In both cases, no such examples were known.

- ‹
- 1
- ›