Salem number

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

Powers of a Salem number ${\alpha }^n(n=1,2,\mathrm{\dots })$ 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
Canonical name	SalemNumber
Date of creation	2013-03-22 13:38:48
Last modified on	2013-03-22 13:38:48
Owner	bbukh (348)
Last modified by	bbukh (348)
Numerical id	6
Author	bbukh (348)
Entry type	Definition
Classification	msc 11R06
Classification	msc 11J71