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Positive points in polar lattices

Published online by Cambridge University Press:  09 April 2009

F. Hossain  and
R. T. Worley
F. Hossain
Affiliation:
Department of Mathematics University of ChittagongChittagong, Bangladesh
R. T. Worley
Affiliation:
Department of Mathematics Monash UniversityVictoria, Australia 3168
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Abstract

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The authors investigate max min μF(x) F(y)for two standard distance functions F in R2, where μ denotes the area of {x ∈ R2; F(x)≤ 1}, the maximum is over all (geometric) lattices Λ in R2 and the minimum is over all positive points x ∈ Λ and y ∈ Λ* (the polar lattice of Λ). An application is given to a problem on fractional parts.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 3 , November 1978 , pp. 348 - 352
Copyright
Copyright © Australian Mathematical Society 1978

References

Cassels, J. W. S. (1959), An introduction to the geometry of numbers (Springer-Verlag, Berlin).CrossRefGoogle Scholar