# Math Help - Zeta Question

1. ## Riemann zeta function

Hello,
I'm studying a proof outline of the Prime Number theorem and I get the equality
$Z(s)=-\frac{\zeta'(s)}{\zeta(s)}$
(which is equal to the Dirichlet serie of the von Mangoldt function Lambda)
The author says that
$\zeta$ and $Z(s)$ are of the same kind where the fraction is defined but I do not see why...

Could someone give me a piece of advice ?