On multiplicatively dependent vectors of polynomial values

Marley Young

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arXiv · 2402.13704

On multiplicatively dependent vectors of polynomial values

Marley Young

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Abstract

Given polynomials $f_1,\ldots,f_n$ in $m$ variables with integral coefficients, we give upper bounds for the number of integral $m$-tuples $\mathbf{u}_1,\ldots, \mathbf{u}_n$ of bounded height such that $f_1(\mathbf{u}_1), \ldots, f_n(\mathbf{u}_n)$ are multiplicatively dependent. We also prove, under certain conditions, a finiteness result for $\mathbf{u} \in \mathbb{Z}^m$ with relatively prime entries such that $f_1(\mathbf{u}),\ldots,f_n(\mathbf{u})$ are multiplicatively dependent.

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Marley Young. 2024-02-21. On multiplicatively dependent vectors of polynomial values. https://arxiv.org/abs/2402.13704

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