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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 College Cambridge
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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 y1 y2, …, yn be any real numbers. We identify the n-tuplet (x1 x2, …, 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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Footnotes

†

This paper and the succeeding one, referred to as II, are shortended versions of chapters of the author's Ph.D. thesis (1953). This thesis itself is available in the University Library, Cambridge.

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.Google 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.Google 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