On small densities defined without pseudorandomness
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913344190939136 |
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| author | Karam, Thomas |
| author_facet | Karam, Thomas |
| contents | We identify an assumption on linear forms $ϕ_1, \dots, ϕ_k: \mathbb{F}_p^n \to \mathbb{F}_p$ that is much weaker than approximate joint equidistribution on the Boolean cube $\{0,1\}^n$ and is in a sense almost as weak as linear independence, but which guarantees that every subset of $\{0,1\}^n$ on which none of $ϕ_1, \dots, ϕ_k$ has full image has a density which tends to 0 with $k$. This density is at most quasipolynomially small in $k$, a bound that is necessarily close to sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On small densities defined without pseudorandomness Karam, Thomas Number Theory Combinatorics Probability We identify an assumption on linear forms $ϕ_1, \dots, ϕ_k: \mathbb{F}_p^n \to \mathbb{F}_p$ that is much weaker than approximate joint equidistribution on the Boolean cube $\{0,1\}^n$ and is in a sense almost as weak as linear independence, but which guarantees that every subset of $\{0,1\}^n$ on which none of $ϕ_1, \dots, ϕ_k$ has full image has a density which tends to 0 with $k$. This density is at most quasipolynomially small in $k$, a bound that is necessarily close to sharp. |
| title | On small densities defined without pseudorandomness |
| topic | Number Theory Combinatorics Probability |
| url | https://arxiv.org/abs/2405.04391 |