Periodic expansion of one by Salem numbers

Shigeki Akiyama; Hachem Hichri

Periodic expansion of one by Salem numbers

Number Theory 2022-08-16 v5 Dynamical Systems

Authors: Shigeki Akiyama , Hachem Hichri

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 $4$ .

Keywords

Salem number Parry number periodic expansion natural density discretized rotation

Cite

@article{arxiv.2206.06675,
  title  = {Periodic expansion of one by Salem numbers},
  author = {Shigeki Akiyama and Hachem Hichri},
  journal= {arXiv preprint arXiv:2206.06675},
  year   = {2022}
}

Comments

Revision after referee comments and suggestions. Information in the paper is increased

Periodic expansion of one by Salem numbers

Abstract

Keywords

Cite

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