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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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Contributor : Pierre Lezowski Connect in order to contact the contributor
Submitted on : Tuesday, October 2, 2012 - 4:55:40 PM
Last modification on : Saturday, December 4, 2021 - 3:42:24 AM
Long-term archiving on: : Thursday, January 3, 2013 - 7:00:08 AM


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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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