A non-linear Roth theorem for thick Cantor sets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908780325765120 |
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| author | McDonald, Alex Nguyen, Micah |
| author_facet | McDonald, Alex Nguyen, Micah |
| contents | We prove that for any function $f$ satisfying certain mild conditions and any Cantor set $K$ with Newhouse thickness greater than $1$, there exists $x\in K$ and $t>0$ such that \[ \{x-t,x,x+f(t)\}\subset K. \] This is an extension of previous work on the existence of three-term arithmetic progressions in Cantor sets to the non-linear setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A non-linear Roth theorem for thick Cantor sets McDonald, Alex Nguyen, Micah Classical Analysis and ODEs 28A80 We prove that for any function $f$ satisfying certain mild conditions and any Cantor set $K$ with Newhouse thickness greater than $1$, there exists $x\in K$ and $t>0$ such that \[ \{x-t,x,x+f(t)\}\subset K. \] This is an extension of previous work on the existence of three-term arithmetic progressions in Cantor sets to the non-linear setting. |
| title | A non-linear Roth theorem for thick Cantor sets |
| topic | Classical Analysis and ODEs 28A80 |
| url | https://arxiv.org/abs/2509.17880 |