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arXiv · 2607.19917

Multiplicative dependence modulo subsets

Min Sha
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Abstract

In this paper, we show that if the non-constant rational functions $f_1, \ldots, f_n\in K(x)$ over a number field $K$ cannot multiplicatively generate a power of a linear fractional function, then there are only finitely many elements $\alpha \in K$ such that $f_1(\alpha),\ldots,f_n(\alpha)$ are multiplicatively dependent modulo some subset `close' (with respect to the Weil height) to the division group of a finitely generated multiplicative subgroup of $K$. This improves some previous results.

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Min Sha. 2026-07-22. Multiplicative dependence modulo subsets. https://arxiv.org/abs/2607.19917

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