An upper bound on the multiplicative energy

2008/06/05 by József Solymosi, Jozsef Solymosi, Solymosi, Jozsef · 2 citations
Computer Science · Mathematics · #11B75 #68R05 #Analytic Number Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:11B75 #msc:68R05

paper · pdf · doi:10.48550/arxiv.0806.1040

openalex publication_date 2008/06/05 · arxiv created 2008/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the sumset or the productset of any finite set of real numbers, A, is at least |A|^4/3-ε, improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy, E(A,A).

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