Reciprocal zeta function

The reciprocal zeta function is $\dfrac{1}{\zeta(s)}$, where $\zeta$ is the Riemann zeta function.

Properties

Theorem: The following formula holds: $$\dfrac{1}{\zeta(z)} = \displaystyle\sum_{k=1}^{\infty} \dfrac{\mu(k)}{k^z},$$ where $\dfrac{1}{\zeta}$ denotes the reciprocal zeta function, $\zeta$ denotes the Riemann zeta function, and $\mu$ denotes the Mobius function.

Proof: proof goes here █