Liouville lambda

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 █