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Real Number Circle Unit Disk Algebraic Integer Dense Algebraic Conjugates Positive Root Uniformly Distributed

1	Circle
1	Real Number
4	Unit Disk
4	Dense
5	Algebraic Integer
7	Algebraic Conjugates
7	Positive Root
15	Uniformly Distributed

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Salem Number

Salem number is a real algebraic integer $\alpha>1$ whose algebraic conjugates all lie in the unit disk $\{\,z\in\mathbb{C} \,\big\vert\, \vert z\vert\leq 1\,\}$ with at least one on the unit circle $\{\,z\in\mathbb{C}\,\big\vert\,\vert z\vert= 1\,\}$ .

Powers of a Salem number $\alpha^n\ (n=1,2,\dotsc)$ are everywhere dense modulo , but are not uniformly distributed modulo .

The smallest known Salem number is the largest positive root of

$\displaystyle \alpha^{10}+\alpha^9-\alpha^7-\alpha^6-\alpha^5-\alpha^4-\alpha^3+\alpha+1=0.$