Difference between revisions of "Euler product for Riemann zeta"
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==References== | ==References== | ||
* {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Riemann zeta|next=Series for log(riemann zeta) over primes}}: § Introduction (2) | * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Riemann zeta|next=Series for log(riemann zeta) over primes}}: § Introduction (2) | ||
| + | * {{BookReference|Higher Transcendental Functions Volume II|1953|Harry Bateman|prev=Riemann zeta|next=}}: pg. $170$ | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 22:33, 8 July 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)
- 1953: Harry Bateman: Higher Transcendental Functions Volume II ... (previous): pg. $170$
