# Salem number

Salem number is a real algebraic integer^{} $\alpha >1$ whose algebraic conjugates all lie in the unit disk $\{z\in \u2102||z|\le 1\}$ with at least one on the unit circle $\{z\in \u2102||z|=1\}$.

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 |