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The number of non-homogeneous lattice points in plane subsets

Published online by Cambridge University Press:  24 October 2008

Michael Mather
Michael Mather
Affiliation:
16 Parkview Ave., Toronto M4X 1 V9, Canada
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Extract

Let Z2 denote the integer lattice in the plane, let A be a non-singular 2 x 2 matrix and let c ∈ R2. Then G = AZ2 + c is called a grid, and its determinant det G is defined to be det A. The grid G is called a subgrid if G ⊂ Z2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 1 , January 1978 , pp. 25 - 29
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1) Barnes, E. S. and Mather, Michael. The number of non-homogeneous lattice points in subsets of Rn. Math. Proc. Cambridge Philos. Soc. 82 (1977), 265–268.CrossRefGoogle Scholar
(2) Borevich, Z. I. and Shafarevich, I. R. Number Theory (New York, London: Academic Press, 1966).Google Scholar
(3) Jamison, Robert E. Covering finite fields with cosets of subspaces. Journal of Combinatorial Theory (A) 22 (1977), 253–266.CrossRefGoogle Scholar