Geodesic
Totally indefinite Euclidean quaternion fields
Jean-Paul Cerri 1   ; Jérôme Chaubert 2   ; Pierre Lezowski 3
1 Univ. Bordeaux, IMB, UMR 5251 F-33400 Talence, France and CNRS, IMB, UMR 5251 F-33400 Talence, France and INRIA LFANT F-33400 Talence, France
2 rue du Talent 1042 Malapalud, Suisse
3 INRIA LFANT F-33400 Talence, France and CNRS, IMB, UMR 5251 F-33400 Talence, France and Univ. Bordeaux, IMB, UMR 5251 F-33400 Talence, France
Acta Arithmetica, Tome 165 (2014) no. 2, pp. 181-200 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a 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.
DOI : 10.4064/aa165-2-4
Keywords: study euclidean property totally indefinite quaternion fields particular establish complete list norm euclidean fields imaginary quadratic number fields enables exhibit example which gives negative answer question asked eichler proofs theoretical algorithmic

Jean-Paul Cerri  1   ; Jérôme Chaubert  2   ; Pierre Lezowski  3

1 Univ. Bordeaux, IMB, UMR 5251 F-33400 Talence, France and CNRS, IMB, UMR 5251 F-33400 Talence, France and INRIA LFANT F-33400 Talence, France
2 rue du Talent 1042 Malapalud, Suisse
3 INRIA LFANT F-33400 Talence, France and CNRS, IMB, UMR 5251 F-33400 Talence, France and Univ. Bordeaux, IMB, UMR 5251 F-33400 Talence, France 
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     author = {Jean-Paul Cerri and J\'er\^ome Chaubert and Pierre Lezowski},
     title = {Totally indefinite {Euclidean} quaternion fields},
     journal = {Acta Arithmetica},
     pages = {181--200},
     year = {2014},
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     doi = {10.4064/aa165-2-4},
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Jean-Paul Cerri; Jérôme Chaubert; Pierre Lezowski. Totally indefinite Euclidean quaternion fields. Acta Arithmetica, Tome 165 (2014) no. 2, pp. 181-200. doi: 10.4064/aa165-2-4

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