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The inhomogeneous minimum of quadratic forms of signature ± 1

Published online by Cambridge University Press:  24 October 2008

Madhu Raka
Madhu Raka
Affiliation:
Panjab University, Chandigarh, India
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Extract

Let Qr be a real indefinite quadratic form in r variables of determinant D ≠ 0 and of type (r1, r2), 0 < r1 < r, r = r1 + r2, S = r1 − r2 being the signature of Qr. It is known (e.g. Blaney (3)) that, given any real numbers c1, c2,…, cr, there exists a constant C depending only on r and s such that the inequality

has a solution in integers x1, x2, …, xr.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 2 , March 1981 , pp. 225 - 235
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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