Hello,

I'm studying a proof outline of the Prime Number theorem and I get the equality

$\displaystyle Z(s)=-\frac{\zeta'(s)}{\zeta(s)}$

(which is equal to the Dirichlet serie of the von Mangoldt function Lambda)

The author says that$\displaystyle \zeta$ and $\displaystyle Z(s)$ are of the same kind where the fraction is definedbut I do not see why...

Could someone give me a piece of advice ?