二维射影表示的惯性重数界及 $\operatorname{PSL}_2(\mathbb{F}_q)$ 和 $\operatorname{PGL}_2(\mathbb{F}_q)$ 数域个数的界
Inertial multiplicity bounds for two dimensional projective representations and bounds for the number of $\operatorname{PSL}_2(\mathbb{F}_q)$ and $\operatorname{PGL}_2(\mathbb{F}_q)$ number fields
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中文总结 AI 辅助
本文利用Serre模性猜想证明数域计数函数的上界，类比类域论中阿贝尔扩张的计数结果。
中文摘要 AI 辅助
我们利用Serre模性猜想（现为Khare--Wintenberger定理）证明了某些数域计数函数的上界。这些结果与固定或有界判别式的阿贝尔扩张个数的尖锐上界相当，其中Serre模性猜想扮演了类域论的角色。
英文摘要
We prove upper bounds for certain number field counting functions using Serre's modularity conjecture (now a theorem of Khare--Wintenberger). These results are comparable to sharp upper bounds for the number of abelian extensions with fixed or bounded discriminant, with Serre's modularity conjecture playing the role of class field theory.
