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arXiv · 2107.05371

Multiplicative dependence of rational values modulo approximate finitely generated groups

Attila Bérczes·Yann Bugeaud·Kálmán Győry·Jorge Mello·Alina Ostafe·Min Sha
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Abstract

In this paper, we establish some finiteness results about the multiplicative dependence of rational values modulo sets which are `close' (with respect to the Weil height) to division groups of finitely generated multiplicative groups of a number field $K$. For example, we show that under some conditions on rational functions $f_1, \ldots, f_n\in K(X)$, there are only finitely many elements $\alpha \in K$ such that $f_1(\alpha),\ldots,f_n(\alpha)$ are multiplicatively dependent modulo such sets.

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Attila Bérczes, Yann Bugeaud, Kálmán Győry, Jorge Mello, Alina Ostafe, Min Sha. 2021-07-12. Multiplicative dependence of rational values modulo approximate finitely generated groups. https://doi.org/10.1017/s0305004124000173

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