Difference between revisions of "Möbius"

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=References=
 
=References=
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1}}: 24.3.1 I.A.
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1}}: $24.3.1 \mathrm{I}.A.$
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 01:35, 22 June 2016

The Möbius function is the function $\mu$ defined by the formula $$\mu(n) = \left\{ \begin{array}{ll} 1 &; n \mathrm{\hspace{2pt}is\hspace{2pt}a\hspace{2pt}squarefree\hspace{2pt}positive\hspace{2pt}integer\hspace{2pt}with\hspace{2pt}even\hspace{2pt}number\hspace{2pt}of\hspace{2pt}prime\hspace{2pt}factors} \\ -1 &; n \mathrm{\hspace{2pt}is\hspace{2pt}a\hspace{2pt}squarefree\hspace{2pt}positive\hspace{2pt}integer\hspace{2pt}with\hspace{2pt}odd\hspace{2pt}number\hspace{2pt}of\hspace{2pt}prime\hspace{2pt}factors} \\ 0 &; n\mathrm{\hspace{2pt}has\hspace{2pt}a\hspace{2pt}square\hspace{2pt}divisor}. \end{array} \right.$$


Properties

Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1
Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta

Videos

Mobius Function Example
Möbius Function - Introduction
Möbius Function - Merten's function
Number Theory 27: Mobius function is multiplicative

References