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- Jean-Paul Cerri
- Math. Comput.
- 2007

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 discriminants, most of which were previously unknown. Tables are given at… (More)

- E. Bayer-Fluckiger, Jean-Paul Cerri, Jérôme Chaubert
- 2009

The notion of Euclidean minimum of a number field is a classical one. In this paper we generalize it to central division algebras and establish some general results in this new context.

- Jean-Paul Cerri
- 2005

- Jean-Paul Cerri
- Math. Comput.
- 2011

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.

- Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski, J.-P. Cerri, J. Chaubert
- 2017

We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish the complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.

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