Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1
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Theorem
The following formula holds for $\mathrm{Re}(z)>1$: $$\dfrac{1}{\zeta(z)} = \displaystyle\sum_{n=1}^{\infty} \dfrac{\mu(n)}{n^z},$$ where $\zeta$ denotes the Riemann zeta function and $\mu$ is the Möbius function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 24.3.1 I.B.