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A structure theorem for sets of small popular doubling, revisited
Published 1 Jun 2015 in math.CO and math.NT | (1506.00448v1)
Abstract: We prove that every set $A\subset\mathbb{Z}/p\mathbb{Z}$ with $\mathbb{E}_x\min(1_A*1_A(x),t)\le(2+\delta)t\mathbb{E}_x 1_A(a)$ is very close to an arithmetic progression. Here $p$ stands for a large prime and $\delta,t$ are small real numbers. This shows that the Vosper theorem is stable in the case of a single set.
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