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arXiv · 2206.06675

Periodic expansion of one by Salem numbers

Shigeki Akiyama·Hachem Hichri
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Abstract

We show that for a Salem number $\beta$ of degree $d$, there exists a positive constant $c(d)$ that $\beta^m$ is a Parry number for integers $m$ of natural density $\ge c(d)$. Further, we show $c(6)>1/2$ and discuss a relation to the discretized rotation in dimension $4$.

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Shigeki Akiyama, Hachem Hichri. 2022-06-14. Periodic expansion of one by Salem numbers. https://arxiv.org/abs/2206.06675

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