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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.10561 |
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| _version_ | 1866918383139684352 |
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| author | Kalitzin, Anne Murru, Nadir |
| author_facet | Kalitzin, Anne Murru, Nadir |
| contents | In this paper, we improve some transcendence results for $p$--adic continued fractions. In particular, we prove that palindromic and quasi--periodic $p$--adic continued fractions converge either to transcendental numbers or quadratic irrationals, removing any restriction on the $p$--adic norm of the partial quotients (or convergents) considered in other works. Moreover, we provide a quantitative version of Ridout's theorem (the $p$--adic analogue of Roth's theorem), and we study the growth of denominators of convergents of algebraic numbers, establishing a $p$--adic version of a well--known result of Davenport and Roth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10561 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transcendence of $p$-adic continued fractions and a quantitative $p$-adic Roth theorem Kalitzin, Anne Murru, Nadir Number Theory In this paper, we improve some transcendence results for $p$--adic continued fractions. In particular, we prove that palindromic and quasi--periodic $p$--adic continued fractions converge either to transcendental numbers or quadratic irrationals, removing any restriction on the $p$--adic norm of the partial quotients (or convergents) considered in other works. Moreover, we provide a quantitative version of Ridout's theorem (the $p$--adic analogue of Roth's theorem), and we study the growth of denominators of convergents of algebraic numbers, establishing a $p$--adic version of a well--known result of Davenport and Roth. |
| title | Transcendence of $p$-adic continued fractions and a quantitative $p$-adic Roth theorem |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.10561 |