View source for Logarithmic derivative of Riemann zeta in terms of series over primes

==Theorem==
The following formula holds:
$$\dfrac{\zeta'(z)}{\zeta(z)}=-\displaystyle\sum_{p \hspace{2pt} \mathrm{prime}}\displaystyle\sum_{k=1}^{\infty} \dfrac{\log p}{p^{kz}},$$
where $\zeta$ denotes the [[Riemann zeta]] and $\log$ denotes the [[logarithm]].

==Proof==

==References==
* {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Series for log(Riemann zeta) in terms of Mangoldt function|next=Logarithmic derivative of Riemann zeta in terms of Mangoldt function}}: § Introduction $(2{'}{'})$

[[Category:Theorem]]
[[Category:Unproven]]