PlanetMath: Mangoldt function

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Mangoldt function

(Definition)

The Mangoldt function $\Lambda$ is defined by

$\begin{displaymath}\Lambda (n) = \begin{cases} \ln p, &\text{if $n=p^k$, where $... ... a natural number $\geq 1$}\ 0, &\text{otherwise} \end{cases}\end{displaymath}$

The Moebius Inversion Formula leads to the identity $\Lambda (n) = \sum_{d\vert n} \mu (n/d) \ln d = - \sum_{d\vert n} \mu (d) \ln d$ .

"Mangoldt function" is owned by KimJ.

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Other names:

von Mangoldt function

Keywords:

number theory

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Cross-references: identity, Moebius inversion
There are 3 references to this entry.

This is version 5 of Mangoldt function, born on 2001-10-16, modified 2003-03-06.
Object id is 256, canonical name is MangoldtFunction.
Accessed 4010 times total.

Classification:

AMS MSC:

11A25 (Number theory :: Elementary number theory :: Arithmetic functions; related numbers; inversion formulas)

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