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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A table of totally real cubic fields
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by I. O. Angell PDF
Math. Comp. 30 (1976), 184-187 Request permission

Abstract:

In this paper the author describes the construction of a table of totally real cubic number fields. Each field is distinguished by the coefficients of a generating polynomial, the index of this polynomial over the field and the discriminant of the field. The class number and a fundamental pair of units is also given.
References
  • I. O. Angell, A table of complex cubic fields, Bull. London Math. Soc. 5 (1973), 37–38. MR 318099, DOI 10.1112/blms/5.1.37
  • P. BACHMANN, Allgemeine Arithmetik der Zahlkörper, Leipzig, 1905. H. DAVENPORT, "On the product of three homogeneous linear forms. II," Proc. London Math. Soc. (2), v. 44, 1938; pp. 412-431.
  • H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, Bull. London Math. Soc. 1 (1969), 345–348. MR 254010, DOI 10.1112/blms/1.3.345
  • B. N. Delone and D. K. Faddeev, Theory of Irrationalities of Third Degree, Acad. Sci. URSS. Trav. Inst. Math. Stekloff, 11 (1940), 340 (Russian). MR 0004269
  • H. J. Godwin, On totally complex quartic fields with small discriminants, Proc. Cambridge Philos. Soc. 53 (1957), 1–4. MR 82527
  • H. J. Godwin and P. A. Samet, A table of real cubic fields, J. London Math. Soc. 34 (1959), 108–110. MR 100579, DOI 10.1112/jlms/s1-34.1.108
  • D. SHANKS, "Review of I. O. Angell, A table of complex cubic fields," Math. Comp.,v. 29, 1975, pp. 661-665. RMT 33.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 184-187
  • MSC: Primary 12A30
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0401701-6
  • MathSciNet review: 0401701