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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2510.27573 |
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| _version_ | 1866914127072460800 |
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| author | Kowalska, Aleksandra |
| author_facet | Kowalska, Aleksandra |
| contents | Green showed that, conditional on GRH, a subset $A \subseteq [N]$ with $\mid A \mid \gg_ε N^{\frac{11}{12}+ε}$ must contain two elements whose difference is $p-1$ for $p$ a prime. We prove an analogous unconditional result for $\mathbf{F}_2[x]$, improving the exponent to $\frac{7}{8}+ε$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sárközy's theorem in $\mathbf{F}_2[x]$ Kowalska, Aleksandra Number Theory Combinatorics 11B30 (Primary) 11P70, 11T55, 11P55 (Secondary) Green showed that, conditional on GRH, a subset $A \subseteq [N]$ with $\mid A \mid \gg_ε N^{\frac{11}{12}+ε}$ must contain two elements whose difference is $p-1$ for $p$ a prime. We prove an analogous unconditional result for $\mathbf{F}_2[x]$, improving the exponent to $\frac{7}{8}+ε$. |
| title | Sárközy's theorem in $\mathbf{F}_2[x]$ |
| topic | Number Theory Combinatorics 11B30 (Primary) 11P70, 11T55, 11P55 (Secondary) |
| url | https://arxiv.org/abs/2510.27573 |