A note on classnumber one in pure cubic fields
Authors:
H. C. Williams and Daniel Shanks
Journal:
Math. Comp. 33 (1979), 13171320
MSC:
Primary 12A30; Secondary 1204, 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 classnumber one approximately equal to . We also suggest more elaborate but more efficient algorithms that could be used to extend the data.
 [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]
DANIEL SHANKS, Review of UMT file: "Table of pure cubic fields for ," Math. Comp., v. 30, 1976, pp. 377379.
 [3]
H.
C. Williams, Certain pure cubic fields with
classnumber one, Math. Comp.
31 (1977), no. 138, 578–580. MR 0432591
(55 #5578), http://dx.doi.org/10.1090/S00255718197704325914
 [4]
H.
Eisenbeis, G.
Frey, and B.
Ommerborn, Computation of the 2rank of pure
cubic fields, Math. Comp.
32 (1978), no. 142, 559–569. MR 0480416
(58 #579), http://dx.doi.org/10.1090/S00255718197804804164
 [5]
H.
C. Williams, G.
Cormack, and E.
Seah, Calculation of the regulator of a pure
cubic field, Math. Comp.
34 (1980), no. 150, 567–611. MR 559205
(81d:12003), http://dx.doi.org/10.1090/S00255718198005592057
 [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]
 DANIEL SHANKS, Review of UMT file: "Table of pure cubic fields for ," Math. Comp., v. 30, 1976, pp. 377379.
 [3]
 H. C. WILLIAMS, "Certain pure cubic fields with class number one," Math. Comp., v. 31, 1977, pp. 578580; "Corrigendum," Math. Comp., v. 33, 1979, pp. 847848. MR 0432591 (55:5578)
 [4]
 H. EISENBEIS, G. FREY & B. OMMERBORN, "Computation of the 2rank of pure cubic fields," Math. Comp., v. 32, 1978, pp. 559569. 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905379777
PII:
S 00255718(1979)05379777
Article copyright:
© Copyright 1979 American Mathematical Society
