On higher dimensional integrality and multiplicative dependence in semigroup algebraic dynamics
Number Theory
2026-04-07 v1 Dynamical Systems
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.
Cite
@article{arxiv.2604.03745,
title = {On higher dimensional integrality and multiplicative dependence in semigroup algebraic dynamics},
author = {Jorge Mello and Yu Yasufuku},
journal= {arXiv preprint arXiv:2604.03745},
year = {2026}
}