Euclidean minima of totally real number fields: Algorithmic determination

DOI10.1090/S0025-5718-07-01932-1zbMath1209.11110OpenAlexW2078905834MaRDI QIDQ3433769

Jean-Paul Cerri

Publication date: 2 May 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01932-1

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Euclidean rings and generalizations (13F07) Ordered fields (12J15) Totally real fields (11R80)

Related Items (12)

EXAMPLES OF NORM-EUCLIDEAN IDEAL CLASSES ⋮ Remarks on Euclidean minima ⋮ Totally indefinite Euclidean quaternion fields ⋮ Upper bounds for Euclidean minima of algebraic number fields ⋮ The Euclidean algorithm in quintic and septic cyclic fields ⋮ Computation of Euclidean minima in totally definite quaternion fields ⋮ Computation of the Euclidean minimum of algebraic number fields ⋮ EUCLIDEAN TOTALLY DEFINITE QUATERNION FIELDS OVER THE RATIONAL FIELD AND OVER QUADRATIC NUMBER FIELDS ⋮ A generalization of Voronoi's reduction theory and its application ⋮ Upper bounds for the Euclidean minima of abelian fields ⋮ Some generalized Euclidean and 2-stage Euclidean number fields that are not norm-Euclidean ⋮ NORM-EUCLIDEAN CYCLIC FIELDS OF PRIME DEGREE

Cites Work

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• A computer algorithm for finding new Euclidean number fields
• The Euclidean algorithm in algebraic number fields
• The inhomogeneous minima of binary quadratic forms. II
• Use of a Computer Scan to Prove Q (√2 + √2) and Q (√3 + √2) are Euclidean
• The Euclidean Algorithm in Cubic Number Fields
• On the norm-Euclideanity of \(\mathbb Q\left(\sqrt{2+\sqrt{2+\sqrt 2}}\right)\) and \(\mathbb Q\left(\sqrt{2+\sqrt 2}\right)\)

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