Difference of a Hauptmodul for $Γ_{0}(N)$ and certain Gross-Zagier type CM value formulas

preprint2021arXivOpen access

In this work, we show that the difference of a Hauptmodul for a genus zero group $Γ_{0}(N)$ as a Hilbert 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 Hilbert modular functions and certain Gross-Zagier type CM value formulas.

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Difference of a Hauptmodul for $Γ_{0}(N)$ and certain Gross-Zagier type CM value formulas

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Difference of a Hauptmodul for Γ0(N)Γ_{0}(N)Γ0​(N) and certain Gross-Zagier type CM value formulas

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Difference of a Hauptmodul for $Γ_{0}(N)$ and certain Gross-Zagier type CM value formulas