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Periodic expansion of one by Salem numbers

Published 14 Jun 2022 in math.NT and math.DS | (2206.06675v5)

Abstract: We show that for a Salem number $\beta$ of degree $d$, there exists a positive constant $c(d)$ that $\betam$ 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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Authors (2)

  1. Shigeki Akiyama 
  2. Hachem Hichri 

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