Computation of Euclidean minima in totally definite quaternion fields

Jean-Paul Cerri (1, 2) , Pierre Lezowski (3)

1 LFANT - Lithe and fast algorithmic number theory
2 IMB - Institut de Mathématiques de Bordeaux
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

We describe an algorithm that allows to compute the Euclidean minimum (for the norm form) of any order of a totally definite quaternion field over a number field K of degree strictly greater than 1. Our approach is a generalization of previous work dealing with number fields. The algorithm was practically implemented when K has degree 2.

Domaines: Théorie des nombres [math.NT]

Jean-Paul Cerri, Pierre Lezowski. Computation of Euclidean minima in totally definite quaternion fields. 2017. ⟨hal-01447059v2⟩