Difference between revisions of "Euler product for Riemann zeta"
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==Theorem== | ==Theorem== | ||
The following formula holds for $\mathrm{Re}(z)>1$: | The following formula holds for $\mathrm{Re}(z)>1$: | ||
| − | $$\zeta(z) | + | $$\zeta(z)=\displaystyle\prod_{p \mathrm{\hspace{2pt} prime}} \dfrac{1}{1-p^{-z}},$$ |
where $\zeta$ is the [[Riemann zeta function]]. | where $\zeta$ is the [[Riemann zeta function]]. | ||
Revision as of 19:46, 9 June 2016
Theorem
The following formula holds for $\mathrm{Re}(z)>1$: $$\zeta(z)=\displaystyle\prod_{p \mathrm{\hspace{2pt} prime}} \dfrac{1}{1-p^{-z}},$$ where $\zeta$ is the Riemann zeta function.
Proof
References
- 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction (2)
