Superoptimal continued fractions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912752852795392 |
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| author | Sanderson, Slade |
| author_facet | Sanderson, Slade |
| contents | Motivated by the optimal continued fractions studied independently by Selenius and Bosma, we define and introduce algorithms producing superoptimal continued fraction expansions of irrationals. The convergents of these expansions simultaneously provide arbitrarily good rational approximations and converge arbitrarily quickly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superoptimal continued fractions Sanderson, Slade Number Theory Dynamical Systems 11K50 (Primary) 11J70, 37A44 (Secondary) Motivated by the optimal continued fractions studied independently by Selenius and Bosma, we define and introduce algorithms producing superoptimal continued fraction expansions of irrationals. The convergents of these expansions simultaneously provide arbitrarily good rational approximations and converge arbitrarily quickly. |
| title | Superoptimal continued fractions |
| topic | Number Theory Dynamical Systems 11K50 (Primary) 11J70, 37A44 (Secondary) |
| url | https://arxiv.org/abs/2508.19743 |