A Computational Technique for Determining the Class Number of a Pure Cubic Field

DOI10.2307/2005974zbMath0324.12005OpenAlexW4237645166MaRDI QIDQ4087305

L. Baniuk, Pierre Barrucand, Hugh C. Williams

Publication date: 1976

Full work available at URL: https://doi.org/10.2307/2005974

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Zeta functions and (L)-functions of number fields (11R42) Iwasawa theory (11R23) Software, source code, etc. for problems pertaining to field theory (12-04)

Related Items

Algebraic number fields, Calculation of the Regulator of a Pure Cubic Field, The class-number one problem for some real cubic number fields with negative discriminants, Improving the Speed of Calculating the Regulator of Certain Pure Cubic Fields, Approximating Euler products and class number computation in algebraic function fields, Class number calculation and elliptic unit. I: Cubic case, 3-rank of ambiguous class groups of cubic Kummer extensions, On a conjecture of Lemmermeyer, On 3-Class groups of certain pure cubic fields, The 3-class groups of \(\mathbb{Q}(\sqrt[3{p})\) and its normal closure], Certain Pure Cubic Fields With Class-Number One

Cites Work

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• Cubic fields whose class numbers are not divisible by 3
• A rational genus, class number divisibility, and unit theory for pure cubic fields
• Pure cubic fields whose class numbers are multiples of three
• The rational solutions of the diophantine equation \(Y^2=X^3-D\)
• Ranks of Sylow 3-subgroups of ideal class groups of certain cubic fields
• The Simplest Cubic Fields
• On the 3-Rank of Quadratic Fields and the Euler Product
• A Table of Complex Cubic Fields
• A numerical study of Dedekind's cubic class number formula