On the representation of an integer in Ostrowski and recurrence numeration systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929494081667072 |
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| author | Mittal, Mohit Sharma, Divyum |
| author_facet | Mittal, Mohit Sharma, Divyum |
| contents | We provide an effective upper bound for positive integers with bounded Hamming weights with respect to both a linear recurrence numeration system and an Ostrowski-$α$ numeration system, where $α$ is a quadratic irrational. We prove a similar result for the representation of an integer in two \textit{different} Ostrowski numeration systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the representation of an integer in Ostrowski and recurrence numeration systems Mittal, Mohit Sharma, Divyum Number Theory 11A63, 11D61, 11J86, 11R04, 11R11 We provide an effective upper bound for positive integers with bounded Hamming weights with respect to both a linear recurrence numeration system and an Ostrowski-$α$ numeration system, where $α$ is a quadratic irrational. We prove a similar result for the representation of an integer in two \textit{different} Ostrowski numeration systems. |
| title | On the representation of an integer in Ostrowski and recurrence numeration systems |
| topic | Number Theory 11A63, 11D61, 11J86, 11R04, 11R11 |
| url | https://arxiv.org/abs/2409.06232 |