Examples of norm-Euclidean ideal classes

Pierre Lezowski (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 LFANT - Lithe and fast algorithmic number theory

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.

Domaines: Théorie des nombres [math.NT]

Pierre Lezowski. Examples of norm-Euclidean ideal classes. International Journal of Number Theory, 2012, 8 (5), pp.1315-1333. ⟨10.1142/S1793042112500777⟩. ⟨hal-00634643v2⟩