Average estimate for additive energy in prime field

2011/07/23 by A. Glibichuk, Alexey Glibichuk, Glibichuk, Alexey
Mathematics · #11T23 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11T23

paper · pdf · doi:10.48550/arxiv.1107.4679

19 pages

arxiv created 2011/07/23 · openalex publication_date 2011/07/23 · arxiv updated 2011/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Assume that A⊆ \Fp, B⊆ \Fp^*, \1/4\leqslant(|B|)/(|A|), |A|=p^α, |B|=p^β. We will prove that for p\geqslant p₀(β) one has ∑_{b∈ B}E₊(A, bA)\leqslant 15 p^-\fracmin\β, 1-α\308|A|³|B|. Here E₊(A, bA) is an additive energy between subset A and it's multiplicative shift bA. This improves previously known estimates of this type.

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