Computation of Euclidean minima in totally definite quaternion fields

Abstract : 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.
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Jean-Paul Cerri, Pierre Lezowski. Computation of Euclidean minima in totally definite quaternion fields. International Journal of Number Theory, World Scientific Publishing, 2018. ⟨hal-01447059v3⟩

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