Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-28T13:42:39.602Z Has data issue: false hasContentIssue false

Some extreme forms defined in terms of Abelian groups

Published online by Cambridge University Press:  09 April 2009

E. S. Barnes
Affiliation:
The University of Sydney.
G. E. Wall
Affiliation:
The University of Sydney.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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), 391441.CrossRefGoogle Scholar
[3]Koksma, J. F., Diophantische Approximationen (Springer, 1936).Google Scholar