Integer Points in Large Bodies

Werner Georg Nowak ()
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Werner Georg Nowak: BOKU Wien (University of Natural Resources and Life Sciences, Vienna)

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 583-599 from Springer

Abstract: Abstract For a compact body ℬ $$\mathcal{B}$$ in three-dimensional Euclidean space with sufficiently smooth boundary, the number N ( ℬ ; t ) $$N(\mathcal{B};t)$$ of points with integer coordinates in a linearly enlarged copy t ℬ $$t\mathcal{B}$$ is approximated in first order by the volume v o l ( ℬ ) t 3 $$\mathrm{vol}(\mathcal{B})t^{3}$$ . This article provides a survey on the state of art of research on the lattice discrepancy D ( ℬ ; t ) = N ( ℬ ; t ) − v o l ( ℬ ) t 3 $$D(\mathcal{B};t) = N(\mathcal{B};t) -\mathrm{vol}(\mathcal{B})t^{3}$$ , starting from the classic theory and emphasizing recent developments and advances.

Keywords: Lattice points; Lattice discrepancy; non-convex bodies (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-06554-0_26

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DOI: 10.1007/978-3-319-06554-0_26

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