In Davenport's Multiplicative Number Theory, They defined the order of Integral Functions.
I was trying to see some examples.
While it is clear that the order of the functions $e^z$ is $1$, $e^{z^2}$ is $2$ and $e^{e^z}$ is $\infty$.
I was wondering how can I find the order of the function $f(z)=z$. I can immediately see that this function has order less than $2$.But I am not sure about the exact order of this. Intutively it seems to be $0$.