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Asymmetric inequalities for non-homogeneous ternary quadratic forms†

Published online by Cambridge University Press:  24 October 2008

Vishwa Chander Dumir
Vishwa Chander Dumir
Affiliation:
Ohio State University, U.S.A.
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Extract

A well-known theorem of Minkowski on the product of two linear forms states that if

are two linear forms with real coefficients and determinant Δ = |αδ − βγ| ≠ 0, then given any real numbers c1, c2 we can find integers x, y such that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 291 - 303
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Barnes, E. S.The positive values of inhomogeneous ternary quadratic forms. J. Australian Math. Soc. 2 (1961), 127–132.CrossRefGoogle Scholar
(2)Cassels, J. W. S.An introduction to the geometry of numbers (Grundlehren, Bd 99, 1959).Google Scholar
(3)Cassels, J. W. S.An introduction to Diophantine approximation (Cambridge University Press, 1957).Google Scholar
(4)Davenport, H.Non-homogeneous ternary quadratic forms. Acta Math. 80 (1948), 65–95.CrossRefGoogle Scholar
(5)Davenport, H.On indefinite ternary quadratic forms. Proc. London Math. Soc. (2) 51 (1949), 145–160.CrossRefGoogle Scholar
(6)Davenport, H. and Heilbronn, H.Asymmetric inequalities for non-homogeneous linear forms. J. London Math. Soc. 22 (1947), 53–61.Google Scholar