English

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.

Keywords

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}
}

Comments

16 pages

R2 v1 2026-06-21T10:28:09.213Z