Difference between revisions of "Series for log(Riemann zeta) in terms of Mangoldt function"
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Revision as of 05:34, 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): § Introduction (2')