A table of totally real cubic fields

Author:
I. O. Angell

Journal:
Math. Comp. **30** (1976), 184-187

MSC:
Primary 12A30

DOI:
https://doi.org/10.1090/S0025-5718-1976-0401701-6

MathSciNet review:
0401701

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**I. O. ANGELL, "A table of complex cubic fields,"*Bull. London Math. Soc.*, v. 5, 1973, pp. 37-38. 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. 412-431.**[4]**H. DAVENPORT & H. HEILBRONN, "On the density of discriminants of cubic fields,"*Bull. London Math. Soc.*, v. 1, 1969, pp. 345-348. 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. 1-4. 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. 108-110. 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. 661-665. RMT 33.

Retrieve articles in *Mathematics of Computation*
with MSC:
12A30

Retrieve articles in all journals with MSC: 12A30

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0401701-6

Article copyright:
© Copyright 1976
American Mathematical Society