2016/03/22 by Oliver Roche‐Newton, Oliver Roche-Newton, Roche-Newton, Oliver · 1 citation
Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Number Theory (math.NT) #math.CO #math.NT
paper · pdf · doi:10.48550/arxiv.1603.06827
This paper has now been superseded by arXiv:1703.09549
openalex publication_date 2016/03/22 · arxiv created 2017/04/04 · arxiv updated 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result in this paper concerns a new five-variable expander. It is proven that for any finite set of real numbers A, |\(a1+a2+a3+a4)2+log a5 :a1,a2,a3,a4,a5 ∈ A \| ≫ (|A|2)/(log |A|). This bound is optimal, up to logarithmic factors. The paper also gives new lower bounds for |A(A-A)| and |A(A+A)|, improving on results from arXiv:1312.6438. The new bounds are |A(A-A)| \gtrapprox |A|3/2+(1)/(34) and |A(A+A)| \gtrapprox |A|3/2+(5)/(242).