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A class of D-extreme Minkowski-reduced forms

Published online by Cambridge University Press:  09 April 2009

D. W. Trenerry
D. W. Trenerry
Affiliation:
The University of New South Wales, Broken Hill, 2880, Australia
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Abstract

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Barnes (1978, 1979) introduced the concept of a -extreme form, which is a Minkowski-reduced positive definite quadratic form having prescribed diagonal coefficients α1, α2, …, αn and providing a local minimum of the determinant of the form over all such forms. Here a class of forms which are -extreme for all α and all n is described.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 269 - 275
Copyright
Copyright © Australian Mathematical Society 1981

References

Barnes, E. S. (1978), ‘On Minkowski's fundamental inequality for reduced positive quadratic forms (I)’, J. Austral. Math. Soc. (Ser. A) 26, 46–52.CrossRefGoogle Scholar
Barnes, E. S. (1979), ‘On Minkowski's fundamental inequality for reduced positive quadratic forms (II)’, J. Austral. Math. Soc. (Ser. A) 27, 1–6.CrossRefGoogle Scholar
Lekkerkerker, C. G. (1969), Geometry of Numbers (Wolters-Noordhoff, Groningen, 1969).Google Scholar
Van der Waerden, B. L. (1956), ‘Die Reduktionstheorie der positiven quadratischen Formen’, Acta Math 96, 265–309.CrossRefGoogle Scholar
Voronoi, G. (1907), ‘Sur quelques propriétés des formes quadratiques positives parfaites’, J. reine angew. Math. 133, 97–178.Google Scholar