Lattice points on ellipses
type: Item
instance of: scholarly article
title: Lattice points on ellipses
zbMATH Open document ID: 0822.11069
DOI: 10.1215/S0012-7094-94-07629-1
author: Javier Cilleruelo
author: Antonio Córdoba
published in: Duke Mathematical Journal
publication date: 1995-06-11T00:00:00Z
review text: Let \(d\) be a positive integer. The author considers the number of lattice points on small arcs of ellipses \(x^ 2+ dy^ 2=n\). The main result can be described as follows: Consider an arc of length \(n^{1/4- \varepsilon}\) on the ellipse. Then, for every \(\varepsilon>0\), there is a finite constant \(C\) such that the arc contains no more than \(C\) lattice points.
Mathematics Subject Classification ID: 11P21
zbMATH DE Number: 755394
zbMATH Keywords: number of lattice points
zbMATH Keywords: ellipse
reviewed by: Ekkehard Krätzel
MaRDI profile type: Publication
cites work: Trigonometric Polynomials and Lattice Points
cites work: B₂[∞]-sequences of square numbers
cites work: Arcs containing no three lattice points
cites work: The distribution of the lattice points on circles
cites work: \(B_ 2[g]\) sequences whose terms are squares
cites work: Q3925344
cites work: Q5685535
cites work: Q4402415
cites work: Q3265794
cites work: A Cantor-Lebesgue theorem for double trigonometric series
cites work: On Fourier coefficients and transforms of functions of two variables
description: scientific article; zbMATH DE number 755394