Difference between revisions of "Mertens"
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(Created page with "Let $n \in \mathbb{Z}^+$. Define the Mertens function $$M(n)=\displaystyle\sum_{k=1}^n \mu(k),$$ where $\mu$ is the [Möbius function].") |
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Let $n \in \mathbb{Z}^+$. Define the Mertens function | Let $n \in \mathbb{Z}^+$. Define the Mertens function | ||
$$M(n)=\displaystyle\sum_{k=1}^n \mu(k),$$ | $$M(n)=\displaystyle\sum_{k=1}^n \mu(k),$$ | ||
| − | where $\mu$ is the [Möbius function]. | + | where $\mu$ is the [[Möbius function]]. |
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Mertensplot,n=0to2000.png|Graph of $M$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =Properties= | ||
| + | |||
| + | =Videos= | ||
| + | [https://www.youtube.com/watch?v=yiyuu9HiXUI Möbius Function - Merten's function (4 September 2007)]<br /> | ||
| + | [https://www.youtube.com/watch?v=jjuNYAkPVTY Möbius Function - Merten's conjecture (4 September 2007)]<br /> | ||
| + | |||
| + | =References= | ||
| + | |||
| + | {{:Number theory functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 17:41, 12 October 2016
Let $n \in \mathbb{Z}^+$. Define the Mertens function $$M(n)=\displaystyle\sum_{k=1}^n \mu(k),$$ where $\mu$ is the Möbius function.
Graph of $M$.
Properties
Videos
Möbius Function - Merten's function (4 September 2007)
Möbius Function - Merten's conjecture (4 September 2007)
