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arXiv · 1706.05874

On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem

Alina Ostafe·Min Sha·Igor E. Shparlinski·Umberto Zannier
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Abstract

In this paper, we study multiplicative dependence of values of polynomials or rational functions over a number field. As an application, we obtain new results on multiplicative dependence in the orbits of a univariate polynomial dynamical system. We also obtain a broad generalisation of the Northcott theorem replacing the finiteness of preperiodic points from a given number field by the finiteness of initial points with two multiplicatively dependent elements in their orbits.

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Alina Ostafe, Min Sha, Igor E. Shparlinski, Umberto Zannier. 2017-06-19. On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem. https://arxiv.org/abs/1706.05874

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