Hachem Hichri

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math.NT2026

Parry order of Parry numbers

Kevin G Hare, Hachem Hichri

We introduce the \emph{Parry order} $Ord_{P} (β)$ , defined as the largest integer $n$ for which $β^{n}$ is a Parry number. This leads to a natural partition of the set of Perro…

math.NT2022

Periodic expansion of one by Salem numbers

Shigeki Akiyama, Hachem Hichri

We show that for a Salem number $β$ of degree $d$ , there exists a positive constant $c (d)$ that $β^{m}$ is a Parry number for integers $m$ of natural density $\geq c (d)$ . Further, we…