On primitive lattice points in planar domains
نویسندگان
چکیده
منابع مشابه
Primitive Lattice Points in Starlike
This article is concerned with the number B D (x) of integer points with relative prime coordinates in p x D, where x is a large real variable and D is a starlike set in the Euclidean plane. Assuming the truth of the Riemann Hypothesis, we establish an asymptotic formula for B D (x). Applications to certain special geometric and arithmetic problems are discussed .
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This is one form of Kronecker’s theorem [4-j aura, since N can be chosen arbitrarily large, it follows that there are an infinity of integer sets (x, yl, -. . , y,) with x > 0 satisfying (A). For n > 2, it is not possible to strengthen this result by replacing the & in (A), throughout, by any function y/(x) which tends to zero as x-m (see, e.g., 15) , Kap VII,37, Satz 6). But, in the case n = 1...
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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 prove that the lattice points on the circles x2 + y2 = n are well distributed for most circles containing lattice points.
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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: Acta Arithmetica
سال: 2003
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa109-1-1