  The "relating" entwines three problems:
  1. Davenport's Problem, describing pairs of polynomials over Q whose ranges
on Z/p are the same for almost all p.
  2. Showing that the monodromy groups of rational function maps over the
complexes are limited to a finite set of groups, outside of groups close to
alternating groups (example, symmetric groups) with special representations,
and dihedral and cyclic groups.
  3. Relating the genus 0 modular curves to the character group of the Monster
simple group, so-called Monstrous Moonshine.
http://www.math.uci.edu/~mfried/pathlist-cov/thomp-genus0.html has a more
detailed exposition on the paper;
http://www.math.uci.edu/~mfried/deflist-cov/Genus0-Prob.html gives a separate
description of genus 0 problem #2.
