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Lattice points in a convex Set of given width

Published online by Cambridge University Press:  09 April 2009

G. B. Elkington  and
J. Hammer
G. B. Elkington
Affiliation:
Department of Pure Mathematics, University of Sydney N.S.W., Australia
J. Hammer
Affiliation:
Department of Pure Mathematics, University of Sydney N.S.W., Australia
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Let S be a closed bounded convex set in d-dimensional Euclidean space Ed. The width w(S) of S is the minimum distance between supporting hyperplanes of S, and L(S) is the number of integral lattice points in the interior of S.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 4 , June 1976 , pp. 504 - 507
Copyright
Copyright © Australian Mathematical Society 1976

References

Niven, I. and Zuckerman, H. S., (1967), ‘Lattice points in regions’, Proc. Amer. Math. Soc. 18, 364–370.CrossRefGoogle Scholar
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Scott, P. R. (1973), ‘A lattice problem in the plane’, Mathematika 20, 247–252.CrossRefGoogle Scholar