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Difference of a Hauptmodul for Γ0(N) and certain Gross-Zagier type CM value formulas

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Abstract

In this work, we show that the difference of a Hauptmodul for a genus zero group Γ0(N) as a modular function on Y0(N) × Y0(N) is a Borcherds lift of type (2, 2). As applications, we derive the Monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11901586), the Natural Science Foundation of Guangdong Province (Grant No. 2019A1515011323) and the Sun Yat-sen University Research Grant for Youth Scholars (Grant No. 19lgpy244). The author thanks Professor Tonghai Yang for his guidance and encouragement, and he also thanks Professor Hongbo Yin for his encouragement. The author also thanks the anonymous referees for the useful comments, corrections and suggestions.

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  1. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, China

    Dongxi Ye

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Ye, D. Difference of a Hauptmodul for Γ0(N) and certain Gross-Zagier type CM value formulas. Sci. China Math. 65, 221–258 (2022). https://doi.org/10.1007/s11425-019-1830-3

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