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arXiv · 1810.08967

On the Orbits of Multiplicative Pairs

Oleksiy Klurman·Alexander P. Mangerel
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Abstract

We characterize all pairs of completely multiplicative functions $f,g:\mathbb{N}\to\mathbb{T}$ such that the orbit closure \[\overline{\{(f(n),g(n+1))\}_{n\ge 1}} \neq \mathbb{T}\times \mathbb{T}.\] In so doing, we settle an old conjecture of Zoltán Daróczy and Imre Kátai.

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Oleksiy Klurman, Alexander P. Mangerel. 2018-10-21. On the Orbits of Multiplicative Pairs. https://doi.org/10.2140/ant.2020.14.155

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