# Prime zeta P

From specialfunctionswiki

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?