Weighted Diophantine approximation on manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908827966767104 |
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| author | Beresnevich, Victor Datta, Shreyasi Yang, Lei |
| author_facet | Beresnevich, Victor Datta, Shreyasi Yang, Lei |
| contents | We establish a weighted simultaneous Khintchine-type theorem, both convergence and divergence, for all nondegenerate manifolds, which answers a problem posed in [Math. Ann., 337(4):769-796, 2007]. This extends the main results of [Acta Math., 231:1-30, 2023] and [Ann. of Math. (2), 175(1):187-235, 2012] in the weighted set-up. As a by-product of our method, we also obtain a multiplicative Khintchine-type convergence theorem for all nondegenerate manifolds, which is a simultaneous analogue of the celebrated result of Bernik, Kleinbock, and Margulis for dual approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11045 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted Diophantine approximation on manifolds Beresnevich, Victor Datta, Shreyasi Yang, Lei Number Theory Dynamical Systems We establish a weighted simultaneous Khintchine-type theorem, both convergence and divergence, for all nondegenerate manifolds, which answers a problem posed in [Math. Ann., 337(4):769-796, 2007]. This extends the main results of [Acta Math., 231:1-30, 2023] and [Ann. of Math. (2), 175(1):187-235, 2012] in the weighted set-up. As a by-product of our method, we also obtain a multiplicative Khintchine-type convergence theorem for all nondegenerate manifolds, which is a simultaneous analogue of the celebrated result of Bernik, Kleinbock, and Margulis for dual approximation. |
| title | Weighted Diophantine approximation on manifolds |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2602.11045 |