Examples of norm-Euclidean ideal classes

Pierre Lezowski 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : In 1978, Lenstra defined the notion of Euclidean ideal class. Using a slight modification of an algorithm computing the Euclidean minimum, we give new examples of number fields with norm-Euclidean ideal classes. Extending the results of Cioffari, we also establish the complete list of pure cubic number fields which admit a norm-Euclidean ideal class.
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Pierre Lezowski. Examples of norm-Euclidean ideal classes. International Journal of Number Theory, World Scientific Publishing, 2012, 8 (5), pp.1315-1333. ⟨10.1142/S1793042112500777⟩. ⟨hal-00634643v2⟩

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