Difference between revisions of "Prime zeta P"
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=Properties= | =Properties= | ||
| + | [[Derivative of prime zeta]]<br /> | ||
[[Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta]]<br /> | [[Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta]]<br /> | ||
=Videos= | =Videos= | ||
| − | [https://www.youtube.com/watch?v=3eN9tQX3JJ4 Zeta Function - Part 5 - Prime Zeta Function]<br /> | + | [https://www.youtube.com/watch?v=3eN9tQX3JJ4 Zeta Function - Part 5 - Prime Zeta Function] (15 March 2012)<br /> |
=External links= | =External links= | ||
Latest revision as of 23:29, 17 March 2017
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
Derivative of prime zeta
Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta
Videos
Zeta Function - Part 5 - Prime Zeta Function (15 March 2012)
External links
How does ∑p<xp−s grow asymptotically for Re(s)<1?
Zeta question - prime zeta. Basic calculus
Prime Zeta Function
Prime zeta definition, multiplication by zero
Closed-form of prime zeta values
Zeros of the prime zeta function
Infinite sum of powers of the prime zeta function
Convergence of prime zeta function for R(s)=1?
