Difference between revisions of "Logarithmic derivative of Riemann zeta in terms of Mangoldt function"
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==References== | ==References== | ||
| − | * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Logarithmic derivative of Riemann zeta in terms of series over primes|next= | + | * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Logarithmic derivative of Riemann zeta in terms of series over primes|next=Riemann zeta as integral of monomial divided by an exponential}}: § Introduction $(2{'}{'})$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 09:05, 19 November 2016
Theorem
The following formula holds: $$\dfrac{\zeta'(z)}{\zeta(z)}=-\displaystyle\sum_{k=1}^{\infty} \dfrac{\Lambda(k)}{k^z},$$ where $\zeta$ denotes the Riemann zeta and $\Lambda$ denotes the Mangoldt function.
Proof
References
- 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction $(2{'}{'})$
