Multiplicity of zeros Can you explain me how to get the multiplicity of a zero? 
In particular, I would ask you how to determine the zeros' multiplicity of
$$\cos(\frac{\pi}{2}z)$$
I suppose they are $z = 2k+1, k \in \mathbb{Z}$ and are simple zeros for the function.

If $f(z) = f '(z) = 0$, $f ''(z)\ne0$ , then $z$ is a double zero.
If $f(z) = f '(z) = f ''(z) = 0$, $f '''(z)\ne0$ , then $z$ is a triple zero.
And so on.
Simple zeros are characterized with $f '(z) \ne0$.
This is the case in your example.
