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Some asymmetric inequalities

Published online by Cambridge University Press:  24 October 2008

Hugh Blaney
Affiliation:
Queen Mary CollegeLondon, E. 1

Extract

Let α, β, γ, δ be real numbers with Δ = |αδ −βγ| > 0, and let ξ, η denote the linear forms

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1950

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References

REFERENCES

(1)Davenport, H. and Heilbronn, H.Asymmetric inequalities for non-homogeneous linear forms. J. London Math. Soc. 22 (1947), 5361.CrossRefGoogle Scholar
(2)Davenport, H.Non-homogeneous ternary quadratic forms. Acta Math. 80 (1948), 6595.CrossRefGoogle Scholar
(3)Cassels, J. W. S.The lattice properties of asymmetric hyperbolic regions. Proc. Cambridge Phil. Soc. 44 (1948), 17, 145–54 and 457–62.CrossRefGoogle Scholar
(4)Segre, B.Lattice points in infinite domains. Duke Math. J. 12 (1945), 337–65.CrossRefGoogle Scholar
(5)Robinson, R. M.Unsymmetrical approximation of irrational numbers. Bull. Amer. Math. Soc. 53 (1947), 351–61.CrossRefGoogle Scholar
(6)Robinson, R. M.The critical numbers for unsymmetrical approximation. Bull. Amer. Math. Soc. 54 (1948), 693705.CrossRefGoogle Scholar
(7)Blaney, H.Indefinite quadratic forms in n variables. J. London Math. Soc. 23 (1948), 153–60.CrossRefGoogle Scholar
(8)Davenport, H.Non-homogeneous binary quadratic forms. K. Ned. Akad. Wet. Amsterdam, 49 (1946), 815–21.Google Scholar
(9)Minkowski, H.Diophantische Approximationen (Leipzig und Berlin, 1907), Kapitel II, p. 14.CrossRefGoogle Scholar