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The "relating" entwines three problems:  1. Davenport's Problem, describing pairs of polynomials over Q whose rangeson Z/p are the same for almost all p.  2. Showing that the monodromy groups of rational function maps over thecomplexes are limited to a finite set of groups, outside of groups close toalternating 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 Monstersimple group, so-called Monstrous Moonshine.http://www.math.uci.edu/~mfried/pathlist-cov/thomp-genus0.html has a moredetailed exposition on the paper;http://www.math.uci.edu/~mfried/deflist-cov/Genus0-Prob.html gives a separatedescription of genus 0 problem #2.

Relating two genus 0 problems of John Thompson