PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Totally indefinite Euclidean quaternion fields

Volume 165 / 2014

Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski Acta Arithmetica 165 (2014), 181-200 MSC: Primary 13F07; Secondary 11Y40, 16H05, 16H10. DOI: 10.4064/aa165-2-4

Abstract

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.

Authors

  • Jean-Paul CerriUniv. Bordeaux, IMB, UMR 5251
    F-33400 Talence, France
    and
    CNRS, IMB, UMR 5251
    F-33400 Talence, France
    and
    INRIA LFANT
    F-33400 Talence, France
    e-mail
  • Jérôme Chaubertrue du Talent
    1042 Malapalud, Suisse
    e-mail
  • Pierre LezowskiINRIA LFANT
    F-33400 Talence, France
    and
    CNRS, IMB, UMR 5251
    F-33400 Talence, France
    and
    Univ. Bordeaux, IMB, UMR 5251
    F-33400 Talence, France
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image