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Indefinite quadratic forms

Published online by Cambridge University Press:  26 February 2010

D. Ridout
D. Ridout
Affiliation:
Department of Mathematics, University College, London.
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Extract

Let Q(x1 …, xn) be an indefinite quadratic form in n variables with real coefficients. Suppose that when Q is expressed as a sum of squares of real linear forms, with positive and negative signs, there are r positive signs and n—r negative signs. It was proved recently by Birch and Davenport that, if

then for any ε > 0 the inequality

is soluble in integers x1, …, xn, not all 0.

Type
Research Article
Information
Mathematika , Volume 5 , Issue 2 , December 1958 , pp. 122 - 124
Copyright
Copyright © University College London 1958

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References

* “Indefinite quadratic forms in many variables”, Mathematika, 5 (1958), 8–12CrossRefGoogle Scholar. This paper will be referred to as BD.

† “Indefinite quadratic forms” (to be published in the Proc. London Math. Soc.).