Mangoldt function
MangoldtFunction
2001-10-16 09:15:15
2003-03-06 06:46:04
Definition
number theory
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The Mangoldt function $\Lambda$ is defined by
\[ \Lambda (n) =
\begin{cases}
\ln p, &\text{if $n=p^k$, where $p$ is a prime and $k$ is a natural number $\geq 1$}\\
0, &\text{otherwise}
\end{cases}
\]
The Moebius Inversion Formula leads to the identity $\Lambda (n) = \sum_{d|n} \mu (n/d) \ln d = - \sum_{d|n} \mu (d) \ln d$.