论文标题
$ ϕ $ - 共同点子组的家族
Families of $ϕ$-congruence subgroups of the modular group
论文作者
论文摘要
我们介绍和研究模块化组的有限指数亚组的家族，该子群概括了一致性亚组。这样的组（称为$ ϕ $ - 综合子群）是通过将模块化组的同构$ ϕ $减少为线性代数组模量整数来获得的。特别是，我们检查了两个示例家族，一方面是从地图中引起的，从地图到准联合群体，另一方面，从地图到第四学位的符合性群体。在准联合案件中，我们还提供了对相应模块化形式的详细讨论，该事实是，在这种情况下，曲线塔包含椭圆曲线上的ISEGEN塔$ y^2 = x^3-1728 $，由模块化组的换向器亚组定义。
We introduce and study families of finite index subgroups of the modular group that generalize the congruence subgroups. Such groups, termed $ϕ$-congruence subgroups, are obtained by reducing homomorphisms $ϕ$ from the modular group into a linear algebraic group modulo integers. In particular, we examine two families of examples, arising on the one hand from a map into a quasi-unipotent group, and on the other hand from maps into symplectic groups of degree four. In the quasi-unipotent case we also provide a detailed discussion of the corresponding modular forms, using the fact that the tower of curves in this case contains the tower of isogenies over the elliptic curve $y^2=x^3-1728$ defined by the commutator subgroup of the modular group.
