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Inhomogeneous minimum of indefinite quaternary 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

Let Q (x1, …, xn) be a real indefinite quadratic form in n-variables x1,…, xn with signature (r, s),r + s = n and determinant D ≠ 0. Then it is known (see Blaney (2)) that there exists constant Cr, s depending only on r, s such that given any real numbers c1, …,cn we can find integers x1, …, xn satisfying

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 277 - 290
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Birch, B. J.The inhomogeneous minima of quadratic forms of signature O. Acta Arithmetica, 4 (1958), 85–98.CrossRefGoogle Scholar
(2)Blaney, H.Indefinite quadratic forms in n variables. J. London Math. Soc. 23 (1948), 153–160.Google Scholar
(3)Blaney, H.Some asymmetric inequalities. Proc. Cambridge Philos. Soc. 46 (1950), 359–376.CrossRefGoogle Scholar
(4)Davenport, H.Non-homogeneous ternary quadratic forms. Acta. Math. 80 (1948), 65–95.Google Scholar
(5)Dumir, V. C. Asymmetric inequalities for non-homogeneous ternary quadratic forms. In course of publication.Google Scholar
(6)Oppenheim, A.One sided inequalities for quadratic forms (I) ternary forms. Proc. London Math. Soc. (3) 3 (1953), 328–337.CrossRefGoogle Scholar
(7)Oppenheim, A.One sided inequalities for quadratic quaternary forms (II) quarternary forms. Proc. London Math. Soc. (3) 3 (1953), 417–429.CrossRefGoogle Scholar
(8)Watson, G. L.Indefinite quadratic forms in many variables, inhomogeneous minimum and a generalization. Proc. London Math. Soc. (3) 12 (1962), 564–576.CrossRefGoogle Scholar