题目：Joint distributions of quadratic class groups

报告人：许跃（西安电子科技大学）

时间：2026年11月12日（周四）14:00-15:00

地点：管理科研楼1310

摘要：Gauss's genus theory forces a relation between the \(2\)-class ranks of quadratic fields with nearly the same ramification. In this talk, I will discuss how far this dependence extends beyond the genus-theoretic layer. We consider \(\mathbb Q(\sqrt d)\) and \(\mathbb Q(\sqrt{d_0d})\), where \(d_0\) is a fixed nonzero squarefree integer. Here \(d\) ranges over squarefree integers of a fixed sign, coprime to \(2d_0\) and ordered by absolute value. We prove that the \(4\)-ranks of their narrow class groups are asymptotically independent precisely when \(d_0\neq\pm1\). The joint law then converges to the product of the corresponding Cohen–Lenstra–Gerth distributions. The exceptions are the degenerate case of a single field and the reflection case, whose joint distribution is already known. I will explain how Smith's box method reduces the problem to coupled random matrices and how our truncated moment-inversion method yields their joint limit. This is joint work with Xiuwu Zhu.