Difference between revisions of "Prime zeta P"
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Revision as of 19:33, 15 June 2016
The prime zeta function is defined by $$P(z) = \displaystyle\sum_{p \mathrm{\hspace{2pt} prime}} \dfrac{1}{p^z},$$ where $\mathrm{Re}(z)>1$. It can be extended outside of this domain via analytic continuation.
Graph of $P(x)$ for $x>1$.
Properties
Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta
External links
How does ∑p<xp−s grow asymptotically for Re(s)<1?
