Year: 2025
Type: article
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.
DOI: 10.37236/13691
Author: Ilya D. Shkredov
Institution: Steklov Mathematical Institute
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413136160