| Difference of a Hauptmodul for Γ0(N ) and certain Gross-Zagier type CM value formulas |
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| 作者姓名： | Dongxi Ye |
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| 作者单位： | School of Mathematics（Zhuhai） |
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| 基金项目： | supported by National Natural Science Foundation of China(Grant No.11901586);the Natural Science Foundation of Guangdong Province(Grant No.2019A1515011323);the Sun Yat-sen University Research Grant for Youth Scholars(Grant No.19lgpy244)。 |
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| 摘 要： | 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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| 关 键 词： | Borcherds product the Gross-Zagier CM value formula monster denominator formula modular forms for the Weil representation |
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