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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.25174 |
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| _version_ | 1866914424325931008 |
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| author | Duverney, Daniel Shiokawa, Iekata |
| author_facet | Duverney, Daniel Shiokawa, Iekata |
| contents | Let $t\geq2$ and $k\geq1$ be integers. Let $H_{k}(z)$ with $\left\vert z\right\vert <1$ be the limit of a certain subsequence of the Stern polynomials introduced by Dilcher and Eriksen. We use Mahler's method to prove the algebraic independence of the values at nonzero algebraic points of the functions $H_{k}(z)$ and $H_{k}(z^{t^{k}})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25174 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stern polynomials and algebraic independence Duverney, Daniel Shiokawa, Iekata Number Theory Let $t\geq2$ and $k\geq1$ be integers. Let $H_{k}(z)$ with $\left\vert z\right\vert <1$ be the limit of a certain subsequence of the Stern polynomials introduced by Dilcher and Eriksen. We use Mahler's method to prove the algebraic independence of the values at nonzero algebraic points of the functions $H_{k}(z)$ and $H_{k}(z^{t^{k}})$. |
| title | Stern polynomials and algebraic independence |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.25174 |