Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T11:32:43.597Z Has data issue: false hasContentIssue false
  • English
  • Français

The product of non-homogeneous linear forms. I†

Published online by Cambridge University Press:  24 October 2008

P. A. Samet
P. A. Samet
Affiliation:
Chris's CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

1. Statement of problem and the method of Barnes and Swinnnerton-Dyer. 1·1. Let ξ1, ξ2, … ξn De n real, homogeneous linear forms in the real variables x1, x2,…, xn and of determinant Δ ǂ 0. Let y1y2, …, yn be any real numbers. We identify the n-tuplet (x1x2, …, xn) with the point P, coordinates (x1, x2, …, xn), of n-dimensional space.We write P≡P0 (mod 1) if x1≡y1, x2≡y2, …, xn≡yn (mod 1), and P0 is the point (y1, …, yn).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 3 , July 1954 , pp. 372 - 379
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 Swinnebton-Dyer, H. P. F.The inhomogeneous minima of binary quadratic forms. I. Acta Math. 87 (1952), 259–322.CrossRefGoogle Scholar
(2)Clarke, L. E. On the product of three non-homogeneous linear forms. Proc. Camb. phil. Soc. 47 (1951), 260–5. Also Cambridge Ph.D. thesis, 1953.Google Scholar
(3)Davenport, H.On the product of three non-homogeneous linear forms. Proc. Camb. phil. Soc. 43 (1947), 137–52.CrossRefGoogle Scholar
(4)Tchebotareff, N. G.Algebraisch-Arithmetische Bemerkungen. (Russian, German summary.) Sci. Notes Kazan Univ. 94 (1934), 14–16. (Also abstract of this in Zbl. Math. 18 (1938), 110–11.)Google Scholar