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On Convex Fundamental Regions for a Lattice

Published online by Cambridge University Press:  20 November 2018

A. M. Macbeath
A. M. Macbeath*
Affiliation:
Queen's College, Dundee
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Let ∧ be a lattice in Euclidean n-space, that is, ∧ is a set of points ε1a1 + … + εnan where a1… , an are linearly independent vectors and the ε run over all integers. Let μ denote the Lebesgue measure. A closed convex set F is called a fundamental region for ∧ if the sets F + x (x ∈∧) cover the whole space without overlapping; that is, if F0 is the interior of F, and 0 ≠ x ∈ ∧, then F0 ∩ (F0 + x) = ϕ.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 177 - 178
Copyright
Copyright © Canadian Mathematical Society 1961

References

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