Difference of a Hauptmodul for Gamma0(N) and certain Gross-Zagier type CM value formulas

Abstract: In this work, we show that the difference of a Hauptmodul for a genus zero group $\Gamma_{0}(N)$ as a modular function on $Y_{0}(N)\times Y_{0}(N)$ is a Borcherds lift of type $(2,2)$. As applications, we derive Monster denominator formula like product expansions for these modular functions and certain Gross–Zagier type CM value formulas.