论文标题
关于假想二次田地的伊瓦沙瓦不变的分布的注释
A note on the distribution of Iwasawa invariants of imaginary quadratic fields
论文作者
论文摘要
给定一个奇数的素数$ p $和一个虚构的二次字段$ k $，我们建立了$ k $的$ p $ rank与$ k $的$ p $ lank，以及cyclotomic $ \ mathbb {z} _p $ k $ $ k $的经典$λ$ invariant。利用这种关系，我们证明了根据$λ$ invariants的分布统计结果，该分布根据其判别物进行了订购的假想二次场。我们的某些结果是有条件的，因为它们依靠原始的Cohen- Lenstra启发式方法来分配假想二次领域的班级组。一些结果是无条件的结果，通过利用BYEON，CRAIG等定理获得AD。
Given an odd prime number $p$ and an imaginary quadratic field $K$, we establish a relationship between the $p$-rank of the class group of $K$, and the classical $λ$-invariant of the cyclotomic $\mathbb{Z}_p$-extension of $K$. Exploiting this relationship, we prove statistical results for the distribution of $λ$-invariants for imaginary quadratic fields ordered according to their discriminant. Some of our results are conditional since they rely on the original Cohen--Lenstra heuristics for the distribution of the $p$-parts of class groups of imaginary quadratic fields. Some results are unconditional results ad are obtained by leveraging theorems of Byeon, Craig and others.
