On lattice points in polyhedral cross-sections
نویسندگان
چکیده
منابع مشابه
Lattice Points on Ellipses
Given a square free positive integer d one may consider the arithmetical function rd(n) = #{n = x + dy/x, y ∈ Z} which can also be described as the number of lattice points on the ellipse x + dy = n and it has a natural interpretation inside the ring of algebraic integers of the field Q( √−d). The main purpose of this paper is to analyse closely this function in connection with the distribution...
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We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩lZ (provided it is non-empty) contains a point whose coefficient ofasymmetry with respect to P is at most 8d · (8l+7)2d+1. If, moreover,P is a simplex, then this bound can be improved to 8 · (8l+ 7)d+1.As an application, we deduce new upper bounds on the volume ofa lattice polytope, given its ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1993
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02573965