Moment transference principles and multiplicative diophantine approximation on hypersurfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913797735710720 |
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| author | Chow, Sam Yu, Han |
| author_facet | Chow, Sam Yu, Han |
| contents | We determine the generic multiplicative approximation rate on a hypersurface. There are four regimes, according to convergence or divergence and curved or flat, and we address all of them. Using geometry and arithmetic in Fourier space, we develop a general framework of moment transference principles, which convert Lebesgue data into data for some other measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moment transference principles and multiplicative diophantine approximation on hypersurfaces Chow, Sam Yu, Han Number Theory 11J83 (primary), 42A16 (secondary) We determine the generic multiplicative approximation rate on a hypersurface. There are four regimes, according to convergence or divergence and curved or flat, and we address all of them. Using geometry and arithmetic in Fourier space, we develop a general framework of moment transference principles, which convert Lebesgue data into data for some other measure. |
| title | Moment transference principles and multiplicative diophantine approximation on hypersurfaces |
| topic | Number Theory 11J83 (primary), 42A16 (secondary) |
| url | https://arxiv.org/abs/2408.10911 |