Difference between revisions of "Prime zeta P"

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=Properties=
 
=Properties=
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[[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 />
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=Videos=
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[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.


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?

References