On algebraic independence of three p-adic continued fractions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908933009965056 |
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| author | Ahallal, Sarra Begare, Mohamed Kacha, Ali |
| author_facet | Ahallal, Sarra Begare, Mohamed Kacha, Ali |
| contents | In this paper, we establish sufficient conditions on the elements of the p-adic continued fractions $A$ and $B$ which guarantee that the p-adic continued fractions $A, B $ and $A^{B}$ are algebraically independent over $\mathbb{Q}$. These elements have partial quotients that increase rapidly. We note that these results extend some work of Bundschuh. Furthermore, we give some numerical examples which illustrated the theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_01464 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On algebraic independence of three p-adic continued fractions Ahallal, Sarra Begare, Mohamed Kacha, Ali Number Theory 11J61, 11J70, 11J81 In this paper, we establish sufficient conditions on the elements of the p-adic continued fractions $A$ and $B$ which guarantee that the p-adic continued fractions $A, B $ and $A^{B}$ are algebraically independent over $\mathbb{Q}$. These elements have partial quotients that increase rapidly. We note that these results extend some work of Bundschuh. Furthermore, we give some numerical examples which illustrated the theoretical results. |
| title | On algebraic independence of three p-adic continued fractions |
| topic | Number Theory 11J61, 11J70, 11J81 |
| url | https://arxiv.org/abs/2604.01464 |