Numbers omitting digits in certain base expansions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917954012053504 |
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| author | Yavicoli, Alexia Yu, Han |
| author_facet | Yavicoli, Alexia Yu, Han |
| contents | In DOI:10.1017/etds.2022.2 the author proved that for each integer $k$ there is an implicit number $M > 0$ such that if $b_1, \cdots , b_k$ are multiplicatively independent integers greater than $M$, there are infinitely many integers whose base $b_1, b_2, \cdots , b_k$ expansions all do not have zero digits. In this paper we don't require the multiplicative independence condition and make the result quantitative, getting an explicit value for $M$. We also obtain a result for the case when the missing digit(s) may not be zero. Finally, we extend our method to study various missing-digit sets in an algebraic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numbers omitting digits in certain base expansions Yavicoli, Alexia Yu, Han Number Theory Classical Analysis and ODEs 28A78, 28A80, 28A12, 11B25 In DOI:10.1017/etds.2022.2 the author proved that for each integer $k$ there is an implicit number $M > 0$ such that if $b_1, \cdots , b_k$ are multiplicatively independent integers greater than $M$, there are infinitely many integers whose base $b_1, b_2, \cdots , b_k$ expansions all do not have zero digits. In this paper we don't require the multiplicative independence condition and make the result quantitative, getting an explicit value for $M$. We also obtain a result for the case when the missing digit(s) may not be zero. Finally, we extend our method to study various missing-digit sets in an algebraic setting. |
| title | Numbers omitting digits in certain base expansions |
| topic | Number Theory Classical Analysis and ODEs 28A78, 28A80, 28A12, 11B25 |
| url | https://arxiv.org/abs/2503.09528 |