On a conjecture of Chen and Yui: Fricke groups (with an appendix by Chao Qin)

Abstract: In this work, we establish formulas for the prime decompositions of resultant and discriminant of the ring class polynomial associated with Thompson series for Fricke group $\Gamma_{0}(p)^{+}$ for $p$ prime and imaginary quadratic field, and as a consequence, validate a conjecture of Chen and Yui on the upper bound of prime factors of such resultants and discriminants. All associated numerical conjectures of Chen and Yui are verified using the Magma code for our formulas written by Chao Qin.