Khintchine's theorem for inhomogeneous simultaneous approximation with polynomial decay
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911621611257856 |
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| author | Kim, Seongmin |
| author_facet | Kim, Seongmin |
| contents | Khintchine's theorem on the measure dichotomy for the set of $ψ$-approximable numbers has been generalized to inhomogeneous and higher-dimensional settings. Allen and Ramírez conjectured that the monotonicity condition can be removed in the inhomogeneous $nm=2$ cases. In this paper, we resolve the $(n,m)=(1,2)$ case for $ψ$ satisfying a polynomial decay condition $ψ(q)=O(q^{-δ})$ for some $δ>0.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22689 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Khintchine's theorem for inhomogeneous simultaneous approximation with polynomial decay Kim, Seongmin Number Theory 11J83, 11K60 Khintchine's theorem on the measure dichotomy for the set of $ψ$-approximable numbers has been generalized to inhomogeneous and higher-dimensional settings. Allen and Ramírez conjectured that the monotonicity condition can be removed in the inhomogeneous $nm=2$ cases. In this paper, we resolve the $(n,m)=(1,2)$ case for $ψ$ satisfying a polynomial decay condition $ψ(q)=O(q^{-δ})$ for some $δ>0.$ |
| title | Khintchine's theorem for inhomogeneous simultaneous approximation with polynomial decay |
| topic | Number Theory 11J83, 11K60 |
| url | https://arxiv.org/abs/2604.22689 |