On some properties of Perron numbers

Nikita Sidorov

Let $\theta$ be a real number, $n\in \mathbb{N}$, and $D_n(\theta )=\left\{{\sum }_{k=1}^n{a}_k{\theta }^k\mid a_k\in \{0,\dots ,\lfloor \theta \rfloor \}\right\}.$ Let $\theta$ be a Perron number, that is, an algebr…