Difference between revisions of "Mertens"

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$$M(n)=\displaystyle\sum_{k=1}^n \mu(k),$$
 
$$M(n)=\displaystyle\sum_{k=1}^n \mu(k),$$
 
where $\mu$ is the [[Möbius function]].
 
where $\mu$ is the [[Möbius function]].
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<div align="center">
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<gallery>
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File:Mertensplot,n=0to2000.png|Graph of $M$.
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</gallery>
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</div>
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=Properties=
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=Videos=
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[https://www.youtube.com/watch?v=yiyuu9HiXUI Möbius Function - Merten's function (4 September 2007)]<br />
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[https://www.youtube.com/watch?v=jjuNYAkPVTY Möbius Function - Merten's conjecture (4 September 2007)]<br />
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=References=
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{{:Number theory functions footer}}
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[[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.

Properties

Videos

Möbius Function - Merten's function (4 September 2007)
Möbius Function - Merten's conjecture (4 September 2007)

References

Number theory functions