find points of ramification, hurwitz formula Hi I have the following question:
$$f(z)=4z^2(z-1)^2/(2z-1)^2$$ 
considered as a meromorhic function over $\mathbb{C}_{\infty}$
has as zeros:
$z=0$, $ord_0(f)=2$
$z=1$, $ord_1(f)=2$
and as poles:
$z=1/2$, $ord_{1/2}(f)=2$
$z=\infty$, $ord_{\infty}(f)=2$
Now, considering the associated map to f:
$F:\mathbb{C}_{\infty}\rightarrow \mathbb{C}_{\infty}$, with 
$F(z)=f(z)$, if $z\in\mathbb{C}_{\infty}-\{1/2,\infty\}$,and 
$F(z)=\infty$, if $z=1/2,\infty$
we have that $deg(F)=deg_0(F)=4$
I I apply the Hurwirtz's formula 
$$2g(\mathbb{C}_{\infty})-2=deg(F)(2g(\mathbb{C}_{\infty})-2)+\sum_{p\in\mathbb{X}}{[mult_{p}(F)-1]}$$
I have that -2=4(-2)+4
I would like to know what I am doing wrong?

You haven't found all of the ramification points.  You've found it has multiple zeroes and poles, but it might also be ramified at values other than the zeroes and poles.  You can find the other ramification points by finding the zeroes of the derivative $f'(z)$.
