Abstract
In this article we investigate the numberA(t) of lattice points in\(\sqrt t\) B whereB is a convex body in ℝs (s≥3) which has a smooth boundary with nonzero Gaussian curvature throughout, andt is a large real parameter. We establish an asymptotic formulaA(t)=Vt s/2+O(t λ(s)) (V the volume ofB) which improves upon a classic result ofE. Hlawka [5].
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To Professor Edmund Hlawka on his 75th birthday
This article was written while the first named author was visiting professor at Vienna University, in spring semester 1991.
This paper is part of a research project supported by the Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” (Nr. P7514-PHY).
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Krätzel, E., Nowak, W.G. Lattice points in large convex bodies. Monatshefte für Mathematik 112, 61–72 (1991). https://doi.org/10.1007/BF01321717
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DOI: https://doi.org/10.1007/BF01321717