Large sets with small doubling modulo p are well covered by an arithmetic progression
Number Theory
2009-10-03 v1
Abstract
We prove that there is a small but fixed positive integer e such that for every prime larger than a fixed integer, every subset S of the integers modulo p which satisfies |2S|<(2+e)|S| and 2(|2S|)-2|S|+2 < 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.
Cite
@article{arxiv.0804.0935,
title = {Large sets with small doubling modulo p are well covered by an arithmetic progression},
author = {Oriol Serra and Gilles Zémor},
journal= {arXiv preprint arXiv:0804.0935},
year = {2009}
}
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16 pages