I asked about fixed points of a conformal self-map on compact riemann surface.
Precisely, this question: Fixed points of map $h$ in compact riemann surface
I indicated my idea to solve ... gave me some direction, but I could not proceed.
I found the same question asked here: Number of fixed points of automorphism on Riemann Surface
Curiously it stops in the same place where I stopped.
So I need some help getting out of here! And it looks like I'm going to get a good lesson from Riemann-Roch at the end!