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Calculation of the regulator of a pure cubic field. (English) Zbl 0431.12006


MSC:

11R27 Units and factorization
11R16 Cubic and quartic extensions
12-04 Software, source code, etc. for problems pertaining to field theory
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Full Text: DOI

References:

[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. · Zbl 0324.12005
[2] B. D. Beach, H. C. Williams, and C. R. Zarnke, Some computer results on units in quadratic and cubic fields, Proceedings of the Twenty-Fifth Summer Meeting of the Canadian Mathematical Congress (Lakehead Univ., Thunder Bay, Ont., 1971) Lakehead Univ., Thunder Bay, Ont., 1971, pp. 609 – 648. · Zbl 0348.12003
[3] B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree, Translations of Mathematical Monographs, Vol. 10, American Mathematical Society, Providence, R.I., 1964. · Zbl 0133.30202
[4] Taira Honda, Pure cubic fields whose class numbers are multiples of three, J. Number Theory 3 (1971), 7 – 12. · Zbl 0222.12004 · doi:10.1016/0022-314X(71)90045-X
[5] Ray Steiner, On the units in algebraic number fields, Proceedings of the Sixth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1976) Congress. Numer., XVIII, Utilitas Math., Winnipeg, Man., 1977, pp. 413 – 435. · Zbl 0477.12003
[6] G. F. VORONOI, On a Generalization of the Algorithm of Continued Fractions, Doctoral Dissertation, Warsaw, 1896. (Russian) · Zbl 0347.45021
[7] Hideo Wada, A table of fundamental units of purely cubic fields, Proc. Japan Acad. 46 (1970), 1135 – 1140. · Zbl 0224.12004
[8] H. C. Williams, Certain pure cubic fields with class-number one, Math. Comp. 31 (1977), no. 138, 578 – 580. · Zbl 0356.12004
[9] H. C. Williams and Daniel Shanks, A note on class-number one in pure cubic fields, Math. Comp. 33 (1979), no. 148, 1317 – 1320. · Zbl 0439.12005
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