If A+A is small then AAA is superquadratic

2018/10/25 by Oliver Roche‐Newton, Oliver Roche-Newton, Roche-Newton, Oliver +2
Mathematics · Psychology · #Advanced Topology and Set Theory #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Psychology #math.CO

paper · pdf · doi:10.48550/arxiv.1810.10842

published in arXiv (Cornell University) (Cornell University) · This updated version contains some extra results using the same methods. The main change is the addition of Theorem 1.3, which proves a superquadratic bound for the triple product of a sum set

openalex publication_date 2018/10/25 · arxiv created 2019/04/02 · arxiv updated 2019/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

This note proves that there exists positive constants c₁ and c₂ such that for all finite A ⊂ \mathbb R with |A+A| ≤ |A|^1+c₁ we have |AAA| ≫ |A|^2+c₂.

Citations

• On the number of sums and products
• Few sums, many products

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