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Note On Extreme Forms

Published online by Cambridge University Press:  20 November 2018

E. S. Barnes
E. S. Barnes*
Affiliation:
University of Sydney, Australia
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Let ƒ(x1, … , xn) = Σaijxixj be a positive definite quadratic form of determinant D = |aij|, and let M be the minimum of f for integral x1, … , xn not all zero. The form ƒ is said to be extreme if the ratio Mn/D does not increase when the coefficients aij of f suffer any sufficiently small variation.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 150 - 154
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Coxeter, H. S. M., Extreme forms, Can. J. Math. 3 (1951), 391–441.Google Scholar
2. Hofreiter, N., Ueber Extremformen, Monatsh. Math. Phys. 40 (1933), 129–152.Google Scholar
3. Voronoï, G., Sur quelques propriétés des formes quadratiques positives parfaites, J. reine angew. Math. 188 (1908), 97–178.Google Scholar