Difference between revisions of "Euler product for Riemann zeta"

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

Latest revision as of 05:00, 16 September 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 $\zeta$ denotes Riemann zeta.

Proof

References

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