Section: New Results

Quaternion algebras

Participants : Jean-Paul Cerri, Pierre Lezowski, Aurel Page.

In a joint work with J. Chaubert ([11] ), J.-P. Cerri and P. Lezowski have studied totally definite quaternion fields over number fields which are Euclidean, that is to say that they admit a left or right Euclidean order. In particular, they have established the complete list of totally definite and Euclidean quaternion fields over real quadratic number fields. In this list, all fields are in fact norm-Euclidean. The proofs are both theoretic and algorithmic.

A. Page uploaded a new version of his article [30] on the computation of arithmetic Kleinian groups, incorporating comments from the referee.