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arXiv · 1112.4691

Ergodic Properties of Square-Free Numbers

Francesco Cellarosi·Yakov G. Sinai
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Abstract

We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This implies that this system is not weakly mixing and has zero measure-theoretical entropy.

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Francesco Cellarosi, Yakov G. Sinai. 2013-04-05. Ergodic Properties of Square-Free Numbers. https://arxiv.org/abs/1112.4691

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