Difference between revisions of "Mangoldt"
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The Mangoldt function is defined by the formula | The Mangoldt function is defined by the formula | ||
$$\Lambda(n) = \left\{ \begin{array}{ll} | $$\Lambda(n) = \left\{ \begin{array}{ll} | ||
| − | \log p & | + | \log p, & n=p^k \mathrm{\hspace{2pt}for\hspace{2pt}some\hspace{2pt}prime\hspace{2pt}}p\mathrm{\hspace{2pt}and\hspace{2pt}integer\hspace{2pt}}k\geq 1, \\ |
| − | 0 & | + | 0, & \mathrm{otherwise}. |
\end{array} \right.$$ | \end{array} \right.$$ | ||
Revision as of 05:59, 22 June 2016
The Mangoldt function is defined by the formula $$\Lambda(n) = \left\{ \begin{array}{ll} \log p, & n=p^k \mathrm{\hspace{2pt}for\hspace{2pt}some\hspace{2pt}prime\hspace{2pt}}p\mathrm{\hspace{2pt}and\hspace{2pt}integer\hspace{2pt}}k\geq 1, \\ 0, & \mathrm{otherwise}. \end{array} \right.$$
Graph of $\Lambda$.
Properties
Relationship between logarithm and Mangoldt
Videos
Number Theory 31: Liouville and mangoldt functions
Number theory: Arithmetic functions #1
