Difference between revisions of "Prime zeta P"
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[http://math.stackexchange.com/questions/1537551/zeros-of-the-prime-zeta-function Zeros of the prime zeta function]<br /> | [http://math.stackexchange.com/questions/1537551/zeros-of-the-prime-zeta-function Zeros of the prime zeta function]<br /> | ||
[http://math.stackexchange.com/questions/246770/infinite-sum-of-powers-of-the-prime-zeta-function Infinite sum of powers of the prime zeta function]<br /> | [http://math.stackexchange.com/questions/246770/infinite-sum-of-powers-of-the-prime-zeta-function Infinite sum of powers of the prime zeta function]<br /> | ||
| − | [http://math.stackexchange.com/questions/1615626/convergence-of-prime-zeta-function-for-mathfrak-rs-1 Convergence of prime zeta function for R(s)=1 | + | [http://math.stackexchange.com/questions/1615626/convergence-of-prime-zeta-function-for-mathfrak-rs-1 Convergence of prime zeta function for R(s)=1?]<br /> |
| − | ?]<br /> | ||
=References= | =References= | ||
Revision as of 19:36, 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?
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?
