Diophantine approximation in metric space
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916164457725952 |
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| author | Fraser, Jonathan M. Koivusalo, Henna Ramirez, Felipe A. |
| author_facet | Fraser, Jonathan M. Koivusalo, Henna Ramirez, Felipe A. |
| contents | Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a countable hierarchy of `well-spread' points, which we refer to as abstract rationals. We prove various Jarnik-Besicovitch type dimension bounds and investigate their sharpness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_06776 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Diophantine approximation in metric space Fraser, Jonathan M. Koivusalo, Henna Ramirez, Felipe A. Number Theory Classical Analysis and ODEs Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a countable hierarchy of `well-spread' points, which we refer to as abstract rationals. We prove various Jarnik-Besicovitch type dimension bounds and investigate their sharpness. |
| title | Diophantine approximation in metric space |
| topic | Number Theory Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2105.06776 |