Multiplicative dependence of rational values modulo approximate finitely generated groups

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 $f_1,\dots ,f_n\in K(X)$, there are only finitely many elements $\alpha \in K$ such that $f_1(\alpha ),\dots ,f_n(\alpha )$ are multiplicatively dependent modulo such sets.

20 pages

References in corpus (2)

• On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem
• Multiplicative dependence among iterated values of rational functions modulo finitely generated groups