论文标题
Hurwitz班级编号具有水平和模块化通信
Hurwitz class numbers with level and modular correspondences
论文作者
论文摘要
在本文中，当模块化曲线$ x_0（m）$具有零属时，我们证明了Hurwitz-eichler类型的hurwitz类数字公式，每个级别$ m $。一个关键思想是通过两种不同的方式计算模块化对应关系的相交数量。引入了$γ_0（m）$及其子组$γ_0^{（m'）}（m）$的Atkin-Lehner参与的概括，以计算cusps上模块化对应关系的交点。
In this paper, we prove Hurwitz-Eichler type formulas for Hurwitz class numbers with each level $ M $ when the modular curve $ X_0(M) $ has genus zero. A key idea is to calculate intersection numbers of modular correspondences with the level in two different ways. A generalization of Atkin-Lehner involutions for $ Γ_0(M) $ and its subgroup $ Γ_0^{(M')}(M) $ is introduced to calculate intersection multiplicities of modular correspondences at cusps.
