Difference between revisions of "Series for log(Riemann zeta) in terms of Mangoldt function"
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==References== | ==References== | ||
| − | * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Series for log(riemann zeta) over primes|next=Logarithmic derivative of Riemann zeta in terms of series over primes}}: § Introduction (2') | + | * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Series for log(riemann zeta) over primes|next=Logarithmic derivative of Riemann zeta in terms of series over primes}}: § Introduction $(2')$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 05:42, 5 July 2016
Theorem
The following formula holds: $$\log\left( \zeta(z) \right)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\Lambda(k)}{\log(k) k^z},$$ 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 $(2')$
