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arXiv · 2412.11368

On Fourier coefficients of sets with small doubling

Ilya D. Shkredov
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Abstract

Let $A$ be a subset of a finite abelian group such that $A$ has a small difference set $A-A$ and the density of $A$ is small. We prove that, counter--intuitively, the smallness (in terms of $|A-A|$) of the Fourier coefficients of $A$ guarantees that $A$ is correlated with a large Bohr set. Our bounds on the size and the dimension of the resulting Bohr set are close to exact.

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Ilya D. Shkredov. 2024-12-16. On Fourier coefficients of sets with small doubling. https://arxiv.org/abs/2412.11368

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