Consider $g(z) = w $, where $w^3 - 3w -z = 0 $( $g$ is the inverse of $f(z) = z^3 - 3z$). What are the branching points of $g(z)$? Sketch the scheme of the Riemann surface of $g(z)$
I know that the idea behind branching points is to make a multi-valued function behave like a single-valued function in some regions. But, how do I determine what ought to be the branching points in this case? Is there any procedure for such functions? I have also no clue about how to work out the scheme of the Riemann surface for $g(z)$.