Difference between revisions of "Series for log(riemann zeta) over primes"
From specialfunctionswiki
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Euler product for Riemann zeta|next=Series for log(Riemann zeta) in terms of Mangoldt function}}: § Introduction (2') | + | * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Euler product for Riemann zeta|next=Series for log(Riemann zeta) in terms of Mangoldt function}}: § Introduction $(2')$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 05:42, 5 July 2016
Theorem
The following formula holds: $$\log \left( \zeta(z) \right)=\displaystyle\sum_{p \hspace{2pt} \mathrm{prime}} \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{kp^{mz}},$$ where $\log$ denotes the logarithm and $\zeta$ denotes the Riemann zeta.
Proof
References
- 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction $(2')$
