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Journal Articles Acta Arithmetica Year : 2014

Totally indefinite Euclidean quaternion fields


We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish the complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.
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Dates and versions

hal-01016614 , version 1 (30-06-2014)
hal-01016614 , version 2 (24-10-2014)
hal-01016614 , version 3 (24-10-2014)


  • HAL Id : hal-01016614 , version 3


Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski. Totally indefinite Euclidean quaternion fields. Acta Arithmetica, 2014, 165 (2), pp.181-200. ⟨hal-01016614v3⟩
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