Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-14T21:06:20.237Z Has data issue: false hasContentIssue false

Inhomogeneous minimum of indefinite quaternary quadratic forms

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Birch, B. J.The inhomogeneous minima of quadratic forms of signature O. Acta Arithmetica, 4 (1958), 8598.CrossRefGoogle Scholar
(2)Blaney, H.Indefinite quadratic forms in n variables. J. London Math. Soc. 23 (1948), 153160.Google Scholar
(3)Blaney, H.Some asymmetric inequalities. Proc. Cambridge Philos. Soc. 46 (1950), 359376.CrossRefGoogle Scholar
(4)Davenport, H.Non-homogeneous ternary quadratic forms. Acta. Math. 80 (1948), 6595.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), 328337.CrossRefGoogle Scholar
(7)Oppenheim, A.One sided inequalities for quadratic quaternary forms (II) quarternary forms. Proc. London Math. Soc. (3) 3 (1953), 417429.CrossRefGoogle Scholar
(8)Watson, G. L.Indefinite quadratic forms in many variables, inhomogeneous minimum and a generalization. Proc. London Math. Soc. (3) 12 (1962), 564576.CrossRefGoogle Scholar