A note on class-number one in pure cubic fields

Authors:
H. C. Williams and Daniel Shanks

Journal:
Math. Comp. **33** (1979), 1317-1320

MSC:
Primary 12A30; Secondary 12-04, 12A50

DOI:
https://doi.org/10.1090/S0025-5718-1979-0537977-7

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 class-number 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 & 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]**DANIEL SHANKS, Review of UMT file: "Table of pure cubic fields for ,"*Math. Comp.*, v. 30, 1976, pp. 377-379.**[3]**H. C. WILLIAMS, "Certain pure cubic fields with class number one,"*Math. Comp.*, v. 31, 1977, pp. 578-580; "Corrigendum,"*Math. Comp.*, v. 33, 1979, pp. 847-848. MR**0432591 (55:5578)****[4]**H. EISENBEIS, G. FREY & B. OMMERBORN, "Computation of the 2-rank of pure cubic fields,"*Math. Comp.*, v. 32, 1978, pp. 559-569. 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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DOI:
https://doi.org/10.1090/S0025-5718-1979-0537977-7

Article copyright:
© Copyright 1979
American Mathematical Society