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Lattice coverings and the diagonal group

Published online by Cambridge University Press:  17 April 2009

G. Ramharter
G. Ramharter
Affiliation:
Institut für Analysis, Techn. Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria.
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Abstract

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Let M be any bounded set in n-dimensional Euclidean space. Then almost all n-dimensional lattices L with determinant 1 have the following property: There exists a diagonal transformation D with determinant 1 (depending on L) such that L does not cover space with DM. Moreover, if M has non-empty interior, the exceptional (null-) set contains at least enumerably many diagonally non-equivalent lattices.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 3 , June 1987 , pp. 407 - 414
Copyright
Copyright © Australian Mathematical Society 1987

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