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A note on class-number one in pure cubic fields


Authors: H. C. Williams and Daniel Shanks
Journal: Math. Comp. 33 (1979), 1317-1320
MSC: Primary 12A30; Secondary 12-04, 12A50
MathSciNet review: 537977
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Abstract: We examine a subset of the pure cubic fields wherein individual fields appear to have a probability of having class-number one approximately equal to $ 3/5$. We also suggest more elaborate but more efficient algorithms that could be used to extend the data.


References [Enhancements On Off] (What's this?)

  • [1] PIERRE BARRUCAND, H. C. WILLIAMS & L. BANIUK, "A computational technique for determining the class number of a pure cubic field," Math. Comp., v. 30, 1976, pp. 312-323. MR 0392913 (52:13726)
  • [2] DANIEL SHANKS, Review of UMT file: "Table of pure cubic fields $ Q(\sqrt[3]{D})$ for $ D < {10^4}$ ," Math. Comp., v. 30, 1976, pp. 377-379.
  • [3] H. C. WILLIAMS, "Certain pure cubic fields with class number one," Math. Comp., v. 31, 1977, pp. 578-580; "Corrigendum," Math. Comp., v. 33, 1979, pp. 847-848. MR 0432591 (55:5578)
  • [4] H. EISENBEIS, G. FREY & B. OMMERBORN, "Computation of the 2-rank of pure cubic fields," Math. Comp., v. 32, 1978, pp. 559-569. MR 0480416 (58:579)
  • [5] H. C. WILLIAMS, G. CORMACK & E. SEAH, "Computation of the regulator of a pure cubic field," Math. Comp. (To appear.) MR 559205 (81d:12003)

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DOI: http://dx.doi.org/10.1090/S0025-5718-1979-0537977-7
Article copyright: © Copyright 1979 American Mathematical Society