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 , where is a prime and . The stability of the percentage of these fields having class-number one is examined.

**[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*,*Greater Than*1,*for Fields*,"*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*,"*Math. Comp.*, v. 23, 1969, pp. 213-214.**[7]**DANIEL SHANKS, "Review of UMT File:*Table of Pure Cubic Fields*for ",*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