A note on class-number one in pure cubic fields

Williams, H. C.; Shanks, Daniel

doi:10.1090/S0025-5718-1979-0537977-7

A note on class-number one in pure cubic fields
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by H. C. Williams and Daniel Shanks PDF

Math. Comp. 33 (1979), 1317-1320 Request permission

Abstract:

We examine a subset of the pure cubic fields wherein individual fields appear to have a probability of having class-number one approximately equal to $3/5$. We also suggest more elaborate but more efficient algorithms that could be used to extend the data.

References

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 10.1090/S0025-5718-1976-0392913-9

Math. Comp.

H. C. Williams, Certain pure cubic fields with class-number one, Math. Comp. 31 (1977), no. 138, 578–580. MR 432591, DOI 10.1090/S0025-5718-1977-0432591-4
H. Eisenbeis, G. Frey, and B. Ommerborn, Computation of the $2$-rank of pure cubic fields, Math. Comp. 32 (1978), no. 142, 559–569. MR 480416, DOI 10.1090/S0025-5718-1978-0480416-4
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, DOI 10.1090/S0025-5718-1980-0559205-7