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

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

2008-04-06

arxiv.org/abs/0804.0935v1

Annales de l'institut Fourier, 59 no. 5 (2009), p. 2043-2060

Mathematics

Number Theory

16 pages

Scientific paper

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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