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Mathematics of Computation

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Euclidean minima of totally real number fields: Algorithmic determination

Author: Jean-Paul Cerri
Journal: Math. Comp. 76 (2007), 1547-1575
MSC (2000): Primary 11Y40; Secondary 11R04, 12J15, 13F07
Published electronically: February 27, 2007
MathSciNet review: 2299788
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Abstract: This article deals with the determination of the Euclidean minimum $M(K)$ of a totally real number field $K$ of degree $n\geq 2$, 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 the end of this paper.

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Jean-Paul Cerri
Affiliation: 2, route de Saint-Dié, F-88600 Aydoilles, France

Received by editor(s): May 9, 2004
Received by editor(s) in revised form: February 21, 2006
Published electronically: February 27, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.