# Mangoldt function

The Mangoldt function^{} $\mathrm{\Lambda}$ is defined by

$$\mathrm{\Lambda}(n)=\{\begin{array}{cc}\mathrm{ln}p,\hfill & \text{if}n={p}^{k}\text{, where}p\text{is a prime and}k\text{is a natural number}\ge 1\hfill \\ 0,\hfill & \text{otherwise}\hfill \end{array}$$ |

The Moebius Inversion Formula leads to the identity $\mathrm{\Lambda}(n)={\sum}_{d|n}\mu (n/d)\mathrm{ln}d=-{\sum}_{d|n}\mu (d)\mathrm{ln}d$.

Title | Mangoldt function |
---|---|

Canonical name | MangoldtFunction |

Date of creation | 2013-03-22 11:47:06 |

Last modified on | 2013-03-22 11:47:06 |

Owner | KimJ (5) |

Last modified by | KimJ (5) |

Numerical id | 10 |

Author | KimJ (5) |

Entry type | Definition |

Classification | msc 11A25 |

Classification | msc 18E30 |

Classification | msc 81-00 |

Synonym | von Mangoldt function |