Computation of Euclidean minima in totally definite quaternion fields

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Cerri , Jean-Paul ; Lezowski , Pierre (2017)
  • Publisher: HAL CCSD
  • Subject: Quaternion algebras | [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT] | Norm-Euclidean orders | Norm-Euclidean minimum | MSC: 11Y40, 11R04, 13F07 | Algorithmic number theory | [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

22 pages, some improvements and corrections, especially in Sections 4 and 5.; 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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