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'Salem number'
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| Title of object: |
Salem number |
| Canonical Name: |
SalemNumber |
| Type: |
Definition |
| Created on: |
2003-05-26 01:17:13 |
| Modified on: |
2003-05-26 01:17:13 |
| Classification: |
msc:11R06, msc:11J71 |
Revision comment (for changes between this and next version):
| Changes for correction #2637 ('Salem number'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic} |
Content:
Salem number is a real algebraic integer $\alpha>1$ whose conjugates all lie in the unit disk $\{\,z\in\mathbb{C}\,\bigl|\, |z|\leq 1\,\}$.
Powers of a Salem number $\alpha^n\ (n=1,2,\dotsc)$ are 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*} |
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