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Some extreme forms defined in terms of Abelian groups

Published online by Cambridge University Press:  09 April 2009

E. S. Barnes  and
G. E. Wall
E. S. Barnes
Affiliation:
The University of Sydney.
G. E. Wall
Affiliation:
The University of Sydney.
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Let be a positive definite quadratic form of determinant D, and let M be the minimum of f(x) for integral x ≠ 0. Then we set and the maximum being over all positive forms f in n variables. f is said to be extreme if y γn(f) is a local maximum for varying f, absolutely extreme if y γ(f) is an absolute maximum, i.e. if y γ(f) = γn.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 1 , August 1959 , pp. 47 - 63
Copyright
Copyright © Australian Mathematical Society 1959

References

[1]Barnes, E. S., Criteria for extreme forms, This Journal p. 17.CrossRefGoogle Scholar
[2]Coxeter, H. S. M., Extreme forms, Canad. J. Math. 3 (1951), 391–441.CrossRefGoogle Scholar
[3]Koksma, J. F., Diophantische Approximationen (Springer, 1936).Google Scholar