Hostname: page-component-7bb8b95d7b-l4ctd Total loading time: 0 Render date: 2024-09-11T16:17:43.097Z Has data issue: false hasContentIssue false
  • English
  • Français

The inhomogeneous minima of complex cubic norm forms

Published online by Cambridge University Press:  24 October 2008

H. P. F. Swinnerton-Dyer
H. P. F. Swinnerton-Dyer
Affiliation:
Trinity CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

1. Let K1, K2, K3 be three conjugate* cubic algebraic number fields, of which we shall take K1 to be real and K2, K3 to be complex conjugate. Let ωi1, ωi2, ωi3 the conjugate basis for the integers of Ki. Write

so that ξi runs through the integers of Ki as the xj run independently through the rational integers, and the ξi (i = 1, 2, 3) are conjugate. The determinant of the ξi, regarded as linear forms in the xj, is ± √d, where d is the common discriminant of the fields.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 2 , April 1954 , pp. 209 - 219
Copyright
Copyright © Cambridge Philosophical Society 1954

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Barnes, E. S. and Swinnerton-Dyer, H. P. F.The inhomogeneous minima of binary quadratic forms. I. Acta Math., Stockh., 87 (1952), 259–323.CrossRefGoogle Scholar
(2)Clarke, L. E.Non-homogeneous linear forms associated with algebraic fields. Quart. J. Math. (2), 2 (1951), 308–15.CrossRefGoogle Scholar
(3)Davenport, H.On the product of n linear forms. Proc. Camb. phil. Soc. 49 (1953), 190–3.CrossRefGoogle Scholar