# Reciprocal Riemann zeta in terms of Mobius

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## Theorem

The following formula holds for $\mathrm{Re}(z)>1$: $$\dfrac{1}{\zeta(z)} = \displaystyle\sum_{k=1}^{\infty} \dfrac{\mu(k)}{k^z},$$ where $\zeta$ denotes the Riemann zeta and $\mu$ denotes the Möbius function.