Euler product for Riemann zeta

Theorem

The following formula holds for $\mathrm{Re}(z)>1$: $$\zeta(z)=\displaystyle\sum_{n=1}^{\infty} \dfrac{1}{n^z} = \displaystyle\prod_{p \mathrm{\hspace{2pt} prime}} \dfrac{1}{1-p^{-z}},$$ where $\zeta$ is the Riemann zeta function.

References

• 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction (2)