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

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.**5**(1973), 37–38. MR**0318099**, https://doi.org/10.1112/blms/5.1.37**[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 and H. Heilbronn,*On the density of discriminants of cubic fields*, Bull. London Math. Soc.**1**(1969), 345–348. MR**0254010**, https://doi.org/10.1112/blms/1.3.345**[5]**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****[6]**H. J. Godwin,*On totally complex quartic fields with small discriminants*, Proc. Cambridge Philos. Soc.**53**(1957), 1–4. MR**0082527****[7]**H. J. Godwin and P. A. Samet,*A table of real cubic fields*, J. London Math. Soc.**34**(1959), 108–110. MR**0100579**, https://doi.org/10.1112/jlms/s1-34.1.108**[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