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On the minimum points of a positive quadratic form
Published online by Cambridge University Press: 26 February 2010
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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
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