A lattice point problem and additive number theory
type: Item
instance of: scholarly article
title: A lattice point problem and additive number theory
zbMATH Open document ID: 0838.11020
DOI: 10.1007/BF01299737
author: Noga Alon
author: Moshe Dubiner
published in: Combinatorica
publication date: 1995-11-21T00:00:00Z
review text: Let \(f(n,d)\) denote the minimal number such that every set of \(f(n,d)\) lattice points in a \(d\) dimensional space contains \(n\) points whose centroid (mean) is also a lattice point. Here the estimate \(f(n,d) < (cd \log d)^dn\) is proved, a sharp one for fixed \(d\) and \(n \to \infty\). The proof combines Plünnecke's ideas, expansion properties of graphs with given eigenvalues, and classical exponential sums to evaluate the eigenvalues of certain Cayley graphs.
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 11P99
zbMATH DE Number: 806472
zbMATH Keywords: eigenvalues of Cayley graphs
zbMATH Keywords: lattice points
Wikidata QID: Q60568639
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01299737
OpenAlex ID: W1978948998
description: scientific article; zbMATH DE number 806472