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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
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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

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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