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On the area of planar convex sets containing many lattice points

Published online by Cambridge University Press:  17 April 2009

P. R. Scott
P. R. Scott
Affiliation:
Department of Mathematics, University of Adelaide, Adelaide, South Australia, Australia.
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Abstract

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A classical theorem of van der Corput gives a bound for the volume of a symmetric convex set in terms of the number of lattice points it contains. This theorem is here generalized and extended for a large class of non-symmetric sets in the plane.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 3 , June 1987 , pp. 441 - 454
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Arkinstall, J., Generalizations of Minkowski's theorem in the plane, (Ph.D. thesis, University of Adelaide, South Australia, 1982).Google Scholar
[2]van der Corput, J.G., “Verallgemeinerung einer Mordellschen Beweismethode in der Geometrie der Zahlen”, Acta Arithmetica 2 (1936), 145–146.CrossRefGoogle Scholar
[3]Nosarzewska, M., “Évaluation de la différence entre l'aire d'une region plane convexe et la nombre des points aux coordonnées entières couverte par elle”, Colloq. Math. 1 (1947), 305–311.CrossRefGoogle Scholar
[4]Pick, G., “Geometrisches zur Zahlenlahre”, Sitzungsber Lotos Prag. (2) 19 (1900), 311–319.Google Scholar
[5]Scott, P.R., “An analogue of Minkowski's theorem in the plane”, J. London Math. Soc. 8 (1974), 647–651.CrossRefGoogle Scholar