Certain pure cubic fields with classnumber one
Author:
H. C. Williams
Journal:
Math. Comp. 31 (1977), 578580
MSC:
Primary 12A50; Secondary 12A30, 1204
Erratum:
Math. Comp. 33 (1979), 847848.
Corrigendum:
Math. Comp. 33 (1979), 847848.
MathSciNet review:
0432591
Fulltext PDF Free Access
Abstract 
References 
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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 classnumber one is examined.
 [1]
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 0392913
(52 #13726), http://dx.doi.org/10.1090/S00255718197603929139
 [2]
M.
D. Hendy, The distribution of ideal class
numbers of real quadratic fields, Math.
Comp. 29 (1975), no. 132, 1129–1134. MR 0409402
(53 #13157), http://dx.doi.org/10.1090/S00255718197504094024
 [3]
Richard
B. Lakein, Computation of the ideal class group
of certain complex quartic fields, Math.
Comp. 28 (1974),
839–846. MR 0374090
(51 #10290), http://dx.doi.org/10.1090/S00255718197403740901
 [4]
Richard
B. Lakein, Computation of the ideal class group
of certain complex quartic fields. II, Math.
Comp. 29 (1975),
137–144. Collection of articles dedicated to Derrick Henry Lehmer on
the occasion of his seventieth birthday. MR 0444605
(56 #2955), http://dx.doi.org/10.1090/S00255718197504446054
 [5]
Richard
B. Lakein, Computation of the ideal class group
of certain complex quartic fields. II, Math.
Comp. 29 (1975),
137–144. Collection of articles dedicated to Derrick Henry Lehmer on
the occasion of his seventieth birthday. MR 0444605
(56 #2955), http://dx.doi.org/10.1090/S00255718197504446054
 [6]
DANIEL SHANKS, "Review of UMT File: Class Number of Primes of the Form ," Math. Comp., v. 23, 1969, pp. 213214.
 [7]
DANIEL SHANKS, "Review of UMT File: Table of Pure Cubic Fields for ", Math. Comp., v. 30, 1976, pp. 377379.
 [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. 312323. MR 0392913 (52:13726)
 [2]
 M. D. HENDY, "The distribution of ideal class numbers of real quadratic fields," Math. Comp., v. 29, 1975, pp. 11291134. 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. 839846. 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. 137144. 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. 335336. MR 0444605 (56:2955)
 [6]
 DANIEL SHANKS, "Review of UMT File: Class Number of Primes of the Form ," Math. Comp., v. 23, 1969, pp. 213214.
 [7]
 DANIEL SHANKS, "Review of UMT File: Table of Pure Cubic Fields for ", Math. Comp., v. 30, 1976, pp. 377379.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197704325914
PII:
S 00255718(1977)04325914
Article copyright:
© Copyright 1977
American Mathematical Society
