A computational technique for determining the class number of a pure cubic field

Barrucand, Pierre; Williams, H. C.; Baniuk, L.

doi:10.1090/S0025-5718-1976-0392913-9

A computational technique for determining the class number of a pure cubic field

Authors: Pierre Barrucand, H. C. Williams and L. Baniuk
Journal: Math. Comp. 30 (1976), 312-323
MSC: Primary 12A50; Secondary 12A30, 12A70
DOI: https://doi.org/10.1090/S0025-5718-1976-0392913-9
MathSciNet review: 0392913
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Abstract: Two different computational techniques for determining the class number of a pure cubic field are discussed. These techniques were implemented on an IBM/370-158 computer, and the class number for each pure cubic field $Q({D^{1/3}})$ for $D = 2,3, \ldots ,9999$ was obtained. Several tables are presented which summarize the results of these computations. Some theorems concerning the class group structure of pure cubic fields are also given. The paper closes with some conjectures which were inspired by the computer results.

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