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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Euclidean minima of totally real number fields: Algorithmic determination
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by Jean-Paul Cerri PDF
Math. Comp. 76 (2007), 1547-1575 Request permission

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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Additional Information
  • Jean-Paul Cerri
  • Affiliation: 2, route de Saint-Dié, F-88600 Aydoilles, France
  • Email: jean-paul.cerri@wanadoo.fr
  • Received by editor(s): May 9, 2004
  • Received by editor(s) in revised form: February 21, 2006
  • Published electronically: February 27, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 1547-1575
  • MSC (2000): Primary 11Y40; Secondary 11R04, 12J15, 13F07
  • DOI: https://doi.org/10.1090/S0025-5718-07-01932-1
  • MathSciNet review: 2299788