A structure theorem for sets of small popular doubling, revisited

2015/06/01 by Przemysław Mazur, Mazur, Przemysław
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1506.00448

arxiv created 2015/06/01 · openalex publication_date 2015/06/01 · arxiv updated 2015/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every set A⊂ℤ/pℤ with 𝔼_xmin(1_A*1_A(x),t)≤(2+δ)t𝔼_x 1_A(a) is very close to an arithmetic progression. Here p stands for a large prime and δ,t are small real numbers. This shows that the Vosper theorem is stable in the case of a single set.

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