Difference between revisions of "Prime zeta P"
From specialfunctionswiki
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=External links= | =External links= | ||
[http://math.stackexchange.com/questions/49383/how-does-sum-px-p-s-grow-asymptotically-for-textres-1/ How does ∑p<xp−s grow asymptotically for Re(s)<1?] <br /> | [http://math.stackexchange.com/questions/49383/how-does-sum-px-p-s-grow-asymptotically-for-textres-1/ How does ∑p<xp−s grow asymptotically for Re(s)<1?] <br /> | ||
| + | [http://math.stackexchange.com/questions/504445/zeta-question-prime-zeta-basic-calculus Zeta question - prime zeta. Basic calculus]<br /> | ||
| + | [http://math.stackexchange.com/questions/799590/prime-zeta-function Prime Zeta Function]<br /> | ||
| + | [http://math.stackexchange.com/questions/32974/prime-zeta-definition-multiplication-by-zero Prime zeta definition, multiplication by zero]<br /> | ||
| + | [http://math.stackexchange.com/questions/1029976/closed-form-of-prime-zeta-values Closed-form of prime zeta values]<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/1615626/convergence-of-prime-zeta-function-for-mathfrak-rs-1 Convergence of prime zeta function for R(s)=1 | ||
| + | ?]<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
[http://math.stackexchange.com/questions/1615626/convergence-of-prime-zeta-function-for-mathfrak-rs-1 Convergence of prime zeta function for R(s)=1
?]
