论文标题
班级，循环简单组和算术
Class Numbers, Cyclic Simple Groups and Arithmetic
论文作者
论文摘要
在这里，我们启动一个程序，以系统的方式研究有限群体与算术几何不变的关系。为此，我们首先在Holomorthic Mock Jacobi形式的情况下为有限组引入了一个最佳模块概念。然后，在重量二重要的特殊情况下，我们将主要顺序的循环组分类为最佳模块，其中假想的二次场的班级数量起着重要作用。最后，我们展示了我们建立的分类与素数模块化曲线虚构二次曲折的算术几何形状之间的联系。
Here we initiate a program to study relationships between finite groups and arithmetic-geometric invariants in a systematic way. To do this we first introduce a notion of optimal module for a finite group in the setting of holomorphic mock Jacobi forms. Then we classify optimal modules for the cyclic groups of prime order, in the special case of weight two and index one, where class numbers of imaginary quadratic fields play an important role. Finally we exhibit a connection between the classification we establish and the arithmetic geometry of imaginary quadratic twists of modular curves of prime level.
