平面格的相似子格
Similar sublattices of planar lattices
摘要：
平面格的相似子格可以通过它的乘子环来分类。后者在一般情况下是有理数环，否则是虚二次域中的阶。几类的例子进行了讨论，特别强调具体的结果。特别是，我们推导出狄利克雷级数生成函数的数量不同的相似子格的一个给定的指标，并将它们与各种zeta函数的订单在虚二次域。
英文摘要：
The similar sublattices of a planar lattice can be classified via its multiplier ring. The latter is the ring of rational integers in the generic case, and an order in an imaginary quadratic field otherwise. Several classes of examples are discussed, with special emphasis on concrete results. In particular, we derive Dirichlet series generating functions for the number of distinct similar sublattices of a given index, and relate them to various zeta functions of orders in imaginary quadratic fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
