A table of totally real cubic fields
Author:
I. O. Angell
Journal:
Math. Comp. 30 (1976), 184187
MSC:
Primary 12A30
MathSciNet review:
0401701
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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.
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I.
O. Angell, A table of complex cubic fields, Bull. London Math.
Soc. 5 (1973), 37–38. MR 0318099
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P. BACHMANN, Allgemeine Arithmetik der Zahlkörper, Leipzig, 1905.
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H. DAVENPORT, "On the product of three homogeneous linear forms. II," Proc. London Math. Soc. (2), v. 44, 1938; pp. 412431.
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Davenport and H.
Heilbronn, On the density of discriminants of cubic fields,
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N. Delone and D.
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0004269 (2,349d)
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H.
J. Godwin, On totally complex quartic fields with small
discriminants, Proc. Cambridge Philos. Soc. 53
(1957), 1–4. MR 0082527
(18,565c)
 [7]
H.
J. Godwin and P.
A. Samet, A table of real cubic fields, J. London Math. Soc.
34 (1959), 108–110. MR 0100579
(20 #7009)
 [8]
D. SHANKS, "Review of I. O. Angell, A table of complex cubic fields," Math. Comp.,v. 29, 1975, pp. 661665. RMT 33.
 [1]
 I. O. ANGELL, "A table of complex cubic fields," Bull. London Math. Soc., v. 5, 1973, pp. 3738. MR 47 #6648. MR 0318099 (47:6648)
 [2]
 P. BACHMANN, Allgemeine Arithmetik der Zahlkörper, Leipzig, 1905.
 [3]
 H. DAVENPORT, "On the product of three homogeneous linear forms. II," Proc. London Math. Soc. (2), v. 44, 1938; pp. 412431.
 [4]
 H. DAVENPORT & H. HEILBRONN, "On the density of discriminants of cubic fields," Bull. London Math. Soc., v. 1, 1969, pp. 345348. MR 40 #7223. MR 0254010 (40:7223)
 [5]
 B. N. DELONE & D. K. FADDEEV, The Theory of Irrationalities of the Third Degree, Trudy Mat. Inst. Steklov., v. 11, 1940; English transl., Transl. Math. Monographs, vol. 10, Amer. Math. Soc., Providence, R. I., 1964. MR 2, 349; 28 #3955. MR 0004269 (2:349d)
 [6]
 H. J. GODWIN, "On totally complex quartic fields with small discriminants," Proc. Cambridge Philos. Soc., v. 53, 1957, pp. 14. MR 18, 565. MR 0082527 (18:565c)
 [7]
 H. J. GODWIN & P. A. SAMET, "A table of real cubic fields," J. London Math. Soc., v. 34, 1959, pp. 108110. MR 20 #7009. MR 0100579 (20:7009)
 [8]
 D. SHANKS, "Review of I. O. Angell, A table of complex cubic fields," Math. Comp.,v. 29, 1975, pp. 661665. RMT 33.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197604017016
PII:
S 00255718(1976)04017016
Article copyright:
© Copyright 1976 American Mathematical Society
