Salem number

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 $\alpha^{n}\ (n=1,2,\ldots)$ are everywhere dense modulo $1$, but are not uniformly distributed modulo $1$.

The smallest known Salem number is the largest positive root of

 $\alpha^{10}+\alpha^{9}-\alpha^{7}-\alpha^{6}-\alpha^{5}-\alpha^{4}-\alpha^{3}+% \alpha+1=0.$
Title Salem number SalemNumber 2013-03-22 13:38:48 2013-03-22 13:38:48 bbukh (348) bbukh (348) 6 bbukh (348) Definition msc 11R06 msc 11J71