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arXiv · 2604.03745

On higher dimensional integrality and multiplicative dependence in semigroup algebraic dynamics

Jorge Mello·Yu Yasufuku
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Abstract

We study multiplicative dependence of points in semigroup orbits in higher dimensions. More specifically, we show that the non-density of integral points in semigroup orbits implies sparsity of multiplicative dependence in orbits. This can be viewed as a semigroup dynamical and a higher dimensional version of recent results by B\'{e}rczes, Ostafe, Shparlinski and Silverman, which in turn can be viewed as a generalization of theorems of Northcott and Siegel. We also confirm that the non-density hypothesis of integral points in orbits is implied by Vojta's conjecture.

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Jorge Mello, Yu Yasufuku. 2026-04-04. On higher dimensional integrality and multiplicative dependence in semigroup algebraic dynamics. https://arxiv.org/abs/2604.03745

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