Euclidean totally definite quaternion fields over the rational field and over quadratic number fields

Abstract : In this article we study totally definite quaternion fields over the rational field and over quadratic number fields. We establish a complete list of all such fields which are Euclidean. Moreover, we prove that every field in this list is in fact norm-Euclidean. The proofs are both theoretical and algorithmic.
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Submitted on : Monday, May 13, 2013 - 3:20:21 PM
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Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski. Euclidean totally definite quaternion fields over the rational field and over quadratic number fields. International Journal of Number Theory, World Scientific Publishing, 2013, 9 (3), pp.653-673. ⟨10.1142/S1793042112501540⟩. ⟨hal-00738164v2⟩

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