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On the minimum points of a positive quadratic form

Published online by Cambridge University Press:  26 February 2010

G. L. Watson
Affiliation:
University College, London.
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Extract

Let fn be a positive-definite n-ary quadratic form, with real coefficients. By the minimum of fn, denoted by min fn, is meant as usual the least value of fn(x1, …, xn) for integers xi not all 0. A minimum point of fn is a point x = (x1, …, xn), with integer coordinates, at which fn takes its minimum value. Let Δ (> 0) be the determinant of a set of n minimum points of fn; then in [1] it was proved that

where γn is the Hermite constant. Enough is known about γn to deduce from (1.1), as in [1], that

Type
Research Article
Copyright
Copyright © University College London 1971

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References

1.Davenport, H. and Watson, G. L., “The minimal points of a positive definite quadratic form”, Mathematika, 1 (1954), 1417.CrossRefGoogle Scholar
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