Displaying similar documents to “Class numbers of totally real fields and applications to the Weber class number problem”

On the Gibson Bounds over Finite Fields

V. Budrevich, Mikhail, E. Guterman, Alexander (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 15A15, 15A04. We investigate the Pólya problem on the sign conversion between the permanent and the determinant over finite fields. The main attention is given to the sufficient conditions which guarantee non-existence of sing-conversion. In addition we show that F3 is the only field with the property that any matrix with the entries from the field is convertible. As a result we obtain that over finite fields there are no analogs of...

Totally indefinite Euclidean quaternion fields

Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski (2014)

Acta Arithmetica

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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.