Difference between revisions of "Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta"
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Latest revision as of 19:31, 15 June 2016
Theorem
The following formula holds: $$P(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\mu(k)}{k} \log \zeta(kz),$$ where $P$ denotes the Prime zeta function, $\mu$ denotes the Möbius function, $\log$ denotes the logarithm, and $\zeta$ denotes the Riemann zeta function.
