Small doubling in prime-order groups: From 2.4 to 2.6

JOURNAL OF NUMBER THEORY

卷:217

Article

Lev, Vsevolod F.¹  Shkredov, Ilya D.² 

[1] Univ Haifa, Dept Math, IL-36006 Tivon, Israel

[2] Steklov Math Inst, Ul Gubkina 8, Moscow 119991, Russia

关键词: Sumset;    Additive combinatorics;    Small doubling;   

DOI  :  10.1016/j.jnt.2020.05.009

来源: Elsevier

【 摘 要 】

Improving upon the results of Freiman and Candela-Serra-Spiegel, we show that for a non-empty subset A subset of F-p with p prime and vertical bar A vertical bar < 0.0045p, (i) if vertical bar A + A vertical bar < 2.59 vertical bar A vertical bar - 3 and vertical bar A vertical bar > 100, then A is contained in an arithmetic progression of size vertical bar A + A vertical bar - vertical bar A vertical bar + 1, and (ii) if vertical bar A - A vertical bar < 2.6 vertical bar A vertical bar-3, then A is contained in an arithmetic progression of size vertical bar A - A vertical bar - vertical bar A vertical bar + 1. The improvement comes from using the properties of higher energies. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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