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The simplest cubic fields
Author:
Daniel Shanks
Journal:
Math. Comp. 28 (1974), 1137-1152
MSC:
Primary 12A50; Secondary 12A30
MathSciNet review:
0352049
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Abstract: The cyclic cubic fields generated by  are studied in detail. The regulators are relatively small and are known at once. The class numbers are always of the form  , are relatively large and easy to compute. The class groups are usually easy to determine since one has the theorem that if m is divisible only by  , then the m-rank of the class group is even. Fields with different 3-ranks are treated separately.
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- H. J. GODWIN & P. A. SAMET, "A table of real cubic fields," J. London Math. Soc., v. 34, 1959, pp. 108-110. MR 20 #7009. MR 0100579 (20:7009)
- [2]
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- [4]
- H. J. GODWIN, "The determination of units in totally real cubic fields," Proc. Cambridge Philos. Soc., v. 56, 1960, pp. 318-321. MR 22 #7998. MR 0117216 (22:7998)
- [5]
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- DANIEL SHANKS, "On the conjecture of Hardy and Littlewood concerning the number of primes of the form
 ," Math. Comp., v. 14, 1960, pp. 320-332. MR 22 #10960. MR 0120203 (22:10960)
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- [8]
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- FRANK GERTH III, Sylow 3-Subgroups of Ideal Class Groups of Certain Cubic Fields, Thesis, Princeton University, Princeton, N. J., 1972.
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- P. BARRUCAND & H. COHN, "Remarks on principal factors in a relative cubic field," J. Number Theory, v. 3, 1971, pp. 226-239. MR 43 #1945. MR 0276197 (43:1945)
- [13]
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- [14]
- MORRIS NEWMAN, "A table of the first factor for prime cyclotomic fields," Math. Comp., v. 24, 1970, pp. 215-219. MR 41 #1684. MR 0257029 (41:1684)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1974-0352049-8
PII:
S 0025-5718(1974)0352049-8
Article copyright:
© Copyright 1974 American Mathematical Society
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