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

Oriol Serra (1) , Gilles Zémor (2)

1 Research Group on Graph Theory and Combinatorics [Barcelona]
2 IMB - Institut de Mathématiques de Bordeaux

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.

Domaines: Théorie des nombres [math.NT]

Oriol Serra, Gilles Zémor. Large sets with small doubling modulo p are well covered by an arithmetic progression. Annales de l'Institut Fourier, 2009, 59 (5), pp.2043--2060. ⟨hal-00271197⟩