论文标题
班级不良部分的分布
Distribution of the bad part of class groups
论文作者
论文摘要
Cohen-Lenstra-Martinet启发式方法可以预测$ \ operatotorname {cl} _k [p^\ infty] $ whne $ k $以$γ$ - fields和$ p \ nmid |γ| $运行。在本文中，我们证明了一些关于某些$ p ||γ| $的理想班级组的分布的结果，并证明该行为在质量上与启发式方法的预测在质量上有所不同。对于一般数字字段，我们的结果是基于计数字段的自然猜想。对于Abelian或$ d_4 $ -fields，我们的结果是无条件的。
The Cohen-Lenstra-Martinet Heuristics gives a prediction of the distribution of $\operatorname{Cl}_K[p^\infty]$ whne $K$ runs over $Γ$-fields and $p\nmid|Γ|$. In this paper, we prove several results on the distribution of ideal class groups for some $p||Γ|$, and show that the behaviour is qualitatively different than what is predicted by the heuristics when $p\nmid|Γ|$.We do this by using genus theory and the invariant part of the class group to investigate the algebraic structure of the class group. For general number fields, our result is conditional on a natural conjecture on counting fields. For abelian or $D_4$-fields, our result is unconditional.
