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arXiv · 0804.0935

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

Oriol Serra·Gilles Zémor
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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.

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Oriol Serra, Gilles Zémor. 2008-04-06. Large sets with small doubling modulo p are well covered by an arithmetic progression. https://arxiv.org/abs/0804.0935

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