Diophantine approximation by rational numbers of certain parity types
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911802969817088 |
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| author | Kim, Dong Han Lee, Seul Bee Liao, Lingmin |
| author_facet | Kim, Dong Han Lee, Seul Bee Liao, Lingmin |
| contents | For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd and odd/even rational numbers. We study algorithms to find best approximations by rational numbers of given parities and compare these algorithms with continued fraction expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diophantine approximation by rational numbers of certain parity types Kim, Dong Han Lee, Seul Bee Liao, Lingmin Number Theory 11J04, 11J70 For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd and odd/even rational numbers. We study algorithms to find best approximations by rational numbers of given parities and compare these algorithms with continued fraction expansions. |
| title | Diophantine approximation by rational numbers of certain parity types |
| topic | Number Theory 11J04, 11J70 |
| url | https://arxiv.org/abs/2403.12341 |