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Certain pure cubic fields with class-number one


Author: H. C. Williams
Journal: Math. Comp. 31 (1977), 578-580
MSC: Primary 12A50; Secondary 12A30, 12-04
DOI: https://doi.org/10.1090/S0025-5718-1977-0432591-4
Erratum: Math. Comp. 33 (1979), 847-848.
Corrigendum: Math. Comp. 33 (1979), 847-848.
MathSciNet review: 0432591
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Abstract: A description is given of the results of some calculations performed to determine the class number of each of the pure cubic fields $ Q(\sqrt[3]{q})$, where $ q\;( \equiv - 1\;\pmod 3)$ is a prime and $ q < 35,100$. The stability of the percentage of these fields having class-number one is examined.


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] M. D. HENDY, "The distribution of ideal class numbers of real quadratic fields," Math. Comp., v. 29, 1975, pp. 1129-1134. MR 0409402 (53:13157)
  • [3] R. B. LAKEIN, "Computation of the ideal class group of certain complex quartic fields," Math. Comp., v. 28, 1974, pp. 839-846. MR 51 #10290. MR 0374090 (51:10290)
  • [4] R. B. LAKEIN, "Computation of the ideal class group of certain complex quartic fields. II," Math. Comp., v. 29, 1975, pp. 137-144. MR 0444605 (56:2955)
  • [5] R. B. LAKEIN, "Review of UMT File: Table of Class Numbers, $ h(p)$ Greater Than 1, for Fields $ Q(\sqrt p ),\,p \equiv 1\;\pmod 4 \leqslant 2776817$," Math. Comp., v. 29, 1975, pp. 335-336. MR 0444605 (56:2955)
  • [6] DANIEL SHANKS, "Review of UMT File: Class Number of Primes of the Form $ 4n + 1$," Math. Comp., v. 23, 1969, pp. 213-214.
  • [7] 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.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1977-0432591-4
Article copyright: © Copyright 1977 American Mathematical Society

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