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arXiv · 2603.25174

Stern polynomials and algebraic independence

Daniel Duverney·Iekata Shiokawa
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Abstract

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 $H_{k}(z^{t^{k}})$.

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Daniel Duverney, Iekata Shiokawa. 2026-03-26. Stern polynomials and algebraic independence. https://arxiv.org/abs/2603.25174

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