论文标题
马尔的猜想与多个不变性
Malle's conjecture with multiple invariants
论文作者
论文摘要
我们定义不变式$ \ operatatorName {inv} _1，\ dots，\ operatatorName {inv} _m $ a Galois扩展名的数字字段，该字段带有固定的Galois组。然后，我们以马尔的猜想精神提出了一种启发式，该启发式渐近地预测了满足$ \ permatatorName {inv} _i \ leq x_i $的扩展数量。结果证明了由阿贝里安galois组证明了猜想。我们还描述了精致的Artin导体，这些导体基本上具有与不变的$ \ permatatorName {inv} _1，\ dots，\ pereratatorName {inv} _m $。
We define invariants $\operatorname{inv}_1,\dots,\operatorname{inv}_m$ of Galois extensions of number fields with a fixed Galois group. Then, we propose a heuristic in the spirit of Malle's conjecture which asymptotically predicts the number of extensions that satisfy $\operatorname{inv}_i\leq X_i$ for all $X_i$. The resulting conjecture is proved for abelian Galois groups. We also describe refined Artin conductors that carry essentially the same information as the invariants $\operatorname{inv}_1,\dots,\operatorname{inv}_m$.
