$S$-units and period length of continued fractions of linear recursions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918143396413440 |
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| author | Kumar, Veekesh Singh, Vivek Sprang, Johannes |
| author_facet | Kumar, Veekesh Singh, Vivek Sprang, Johannes |
| contents | Let $(A_n)_{n\in \mathbb{Z}}$ be a linear recurrence sequence with values in a real quadratic field. In this paper, we study the question whether the period length of the continued fraction of $A_n$ is bounded as $n$ varies. The case where $(A_n)_n$ is a linear recurrence of degree $1$ has previously been solved by Corvaja and Zannier. Their result settled a problem posed by Mendès France about the length of the periods of the continued fractions for $α^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $S$-units and period length of continued fractions of linear recursions Kumar, Veekesh Singh, Vivek Sprang, Johannes Number Theory 11J68, 11J87 (Primary), 11B37(Secondary) Let $(A_n)_{n\in \mathbb{Z}}$ be a linear recurrence sequence with values in a real quadratic field. In this paper, we study the question whether the period length of the continued fraction of $A_n$ is bounded as $n$ varies. The case where $(A_n)_n$ is a linear recurrence of degree $1$ has previously been solved by Corvaja and Zannier. Their result settled a problem posed by Mendès France about the length of the periods of the continued fractions for $α^n$. |
| title | $S$-units and period length of continued fractions of linear recursions |
| topic | Number Theory 11J68, 11J87 (Primary), 11B37(Secondary) |
| url | https://arxiv.org/abs/2509.14599 |