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 | References | Similar Articles | Additional Information

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.

- Pierre Barrucand, H. C. Williams, and L. Baniuk,
*A computational technique for determining the class number of a pure cubic field*, Math. Comp.**30**(1976), no. 134, 312–323. MR**392913**, DOI https://doi.org/10.1090/S0025-5718-1976-0392913-9 - M. D. Hendy,
*The distribution of ideal class numbers of real quadratic fields*, Math. Comp.**29**(1975), no. 132, 1129–1134. MR**409402**, DOI https://doi.org/10.1090/S0025-5718-1975-0409402-4 - Richard B. Lakein,
*Computation of the ideal class group of certain complex quartic fields*, Math. Comp.**28**(1974), 839–846. MR**374090**, DOI https://doi.org/10.1090/S0025-5718-1974-0374090-1 - Richard B. Lakein,
*Computation of the ideal class group of certain complex quartic fields. II*, Math. Comp.**29**(1975), 137–144. MR**444605**, DOI https://doi.org/10.1090/S0025-5718-1975-0444605-4 - Richard B. Lakein,
*Computation of the ideal class group of certain complex quartic fields. II*, Math. Comp.**29**(1975), 137–144. MR**444605**, DOI https://doi.org/10.1090/S0025-5718-1975-0444605-4
DANIEL SHANKS, "Review of UMT File:

*Class Number of Primes of the Form*$4n + 1$,"

*Math. Comp.*, v. 23, 1969, pp. 213-214. 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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Article copyright:
© Copyright 1977
American Mathematical Society