On Fourier coefficients of sets with small doubling
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909430197518336 |
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| author | Shkredov, Ilya D. |
| author_facet | Shkredov, Ilya D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Fourier coefficients of sets with small doubling Shkredov, Ilya D. Combinatorics Number Theory 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. |
| title | On Fourier coefficients of sets with small doubling |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2412.11368 |