Totally indefinite Euclidean quaternion fields
Jean-Paul Cerri ; Jérôme Chaubert ; Pierre Lezowski
Acta Arithmetica, Tome 166 (2014), p. 181-200 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:279728 
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     title = {Totally indefinite Euclidean quaternion fields},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {181-200},
     zbl = {1305.16011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-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 166 (2014) pp. 181-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-2-4/