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Minkowski's fundamental inequality for reduced positive quadratic forms

Published online by Cambridge University Press:  09 April 2009

E. S. Barnes
E. S. Barnes
Affiliation:
The University of AdelaideAdelaide, 5001Australia
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Abstract

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Forms which are reduced in the sense of Minkowski satisfy the “fundamental inequality” a11a22 hellipann≤λnD; the best possible value of λn is known for n≤5. A more precise result for the minimum value of D in terms of the diagonal coefficients has been stated by Oppenheim for ternary forms. The corresponding precise result for quaternary forms is established here by considering a convex polytope D(α), defined as the intersection of the cone of reduced forms with the hyperplanes aii = αi (i = 1, hellip n).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1978 , pp. 46 - 52
Copyright
Copyright © Australian Mathematical Society 1978

References

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