Difference between revisions of "Liouville lambda"
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Revision as of 12:09, 19 January 2015
The Liouville function is defined by the formula $$\lambda(n) = (-1)^{\Omega(n)},$$ where $\Omega(n)$ indicates the number of prime factors of $n$, counted with multiplicity.
Properties
Theorem: The following formula holds: $$\dfrac{\zeta(2s)}{\zeta(s)}=\displaystyle\sum_{n=1}^{\infty} \dfrac{\lambda(n)}{n^s},$$ where $\zeta$ denotes the Riemann zeta function.
Proof: proof goes here █
