Salem number
SalemNumber
2003-05-26 01:17:13
2003-10-02 23:05:29
Definition
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Salem number is a real algebraic integer $\alpha>1$ whose algebraic conjugates all lie in the unit disk $\{\,z\in\mathbb{C} \,\big|\, |z|\leq 1\,\}$ with at least one on the unit circle $\{\,z\in\mathbb{C}\,\big|\,|z|= 1\,\}$.
Powers of a Salem number $\alpha^n\ (n=1,2,\dotsc)$ are everywhere dense modulo $1$, but are not uniformly distributed modulo $1$.
The smallest known Salem number is the largest positive root of
\begin{equation*}
\alpha^{10}+\alpha^9-\alpha^7-\alpha^6-\alpha^5-\alpha^4-\alpha^3+\alpha+1=0.
\end{equation*}