Bourgain-Chang's proof of the weak Erdős-Szemerédi conjecture

2017/10/25 by Dmitrii Zhelezov, Zhelezov, Dmitrii
Economics, Econometrics and Finance · Mathematics · #11A05 #Advanced Topology and Set Theory #Analytic Number Theory Research #FOS: Mathematics #Italy: Economic History and Contemporary Issues #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1710.09316

openalex publication_date 2017/10/25 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

This is an exposition of the following `weak' Erdős-Szemerédi conjecture for integer sets proved by Bourgain and Chang in 2004. For any γ> 0 there exists Λ(γ) > 0 such that for an arbitrary A ⊂ ℕ, if |AA| ≤ K|A| then E₊(A) ≤ K^Λ|A|^2+γ.

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