Roth's Theorem in Super Smooth Numbers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914104983158784 |
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| author | Wijaya, Laurence P. |
| author_facet | Wijaya, Laurence P. |
| contents | We say that the set of $y$-smooth numbers $\mathcal{S}(N,y)$ up to $N$ is super smooth if $y=\log^KN$ for a large fixed constant $K$. We show that the Roth's theorem on arithmetic progressions is true in super smooth numbers case. This extends the result of Harper where he showed the statement is true under a weaker hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Roth's Theorem in Super Smooth Numbers Wijaya, Laurence P. Number Theory 11B25, 11L07, 11N25 We say that the set of $y$-smooth numbers $\mathcal{S}(N,y)$ up to $N$ is super smooth if $y=\log^KN$ for a large fixed constant $K$. We show that the Roth's theorem on arithmetic progressions is true in super smooth numbers case. This extends the result of Harper where he showed the statement is true under a weaker hypothesis. |
| title | Roth's Theorem in Super Smooth Numbers |
| topic | Number Theory 11B25, 11L07, 11N25 |
| url | https://arxiv.org/abs/2510.18024 |