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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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https://hal.archives-ouvertes.fr/hal-01447059
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Submitted on : Saturday, July 14, 2018 - 1:20:31 PM
Last modification on : Saturday, December 4, 2021 - 3:43:30 AM
Long-term archiving on: : Tuesday, October 16, 2018 - 1:34:52 AM

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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, 2019, 15 (1), pp.43-66. ⟨10.1142/S1793042118501725⟩. ⟨hal-01447059v3⟩

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