Large sets with small doubling modulo p are well covered by an arithmetic progression

Oriol Serra, Gilles Zémor

Type: Article

Publication Date: 2009-01-01

Citations: 7

DOI: https://doi.org/10.5802/aif.2482

Abstract

We prove that there is a small but fixed positive integer ϵ such that for every prime p larger than a fixed integer, every subset S of the integers modulo p which satisfies |2S|≤(2+ϵ)|S| and 2(|2S|)-2|S|+3≤p is contained in an arithmetic progression of length |2S|-|S|+1. This is the first result of this nature which places no unnecessary restrictions on the size of S.

Locations

arXiv (Cornell University) - View - PDF
French digital mathematics library (Numdam) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View
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Annales de l’institut Fourier - View - PDF

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