Computation of the Euclidean minimum of algebraic number fields

Pierre Lezowski 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We present an algorithm to compute the Euclidean minimum of an algebraic number field, which is a generalization of the algorithm restricted to the totally real case described by Cerri. With a practical implementation, we obtain unknown values of the Euclidean minima of algebraic number fields of degree up to 8 in any signature, especially for cyclotomic fields, and many new examples of norm-Euclidean or non-norm-Euclidean algebraic number fields. We also prove a result of independant interest concerning real quadratic fields whose Euclidean minimum is equal to 1.
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Mathematics of Computation, American Mathematical Society, 2014, 83, pp.1397-1426. 〈10.1090/S0025-5718-2013-02746-9〉
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Contributeur : Pierre Lezowski <>
Soumis le : mardi 2 octobre 2012 - 16:55:40
Dernière modification le : jeudi 11 janvier 2018 - 06:22:36
Document(s) archivé(s) le : jeudi 3 janvier 2013 - 07:00:08

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Pierre Lezowski. Computation of the Euclidean minimum of algebraic number fields. Mathematics of Computation, American Mathematical Society, 2014, 83, pp.1397-1426. 〈10.1090/S0025-5718-2013-02746-9〉. 〈hal-00632997v2〉

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