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Totally indefinite Euclidean quaternion fields

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01016614
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Submitted on : Friday, October 24, 2014 - 3:13:59 PM
Last modification on : Friday, January 21, 2022 - 3:23:02 AM
Long-term archiving on: : Sunday, January 25, 2015 - 10:35:12 AM

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  • HAL Id : hal-01016614, version 3

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

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