Geodesic
On Fourier coefficients of sets with small doubling
Ilya D. Shkredov1
1Steklov Mathematical Institute
The electronic journal of combinatorics, Tome 32 (2025) no. 3
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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.
DOI : 10.37236/13691
Classification : 11B13, 20K01

Ilya D. Shkredov  1

1 Steklov Mathematical Institute 
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     author = {Ilya D. Shkredov},
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Ilya D. Shkredov. On Fourier coefficients of sets with small doubling. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13691

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