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arXiv · 2609.10245

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

Brandon Alberts
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Abstract

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.

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Brandon Alberts. 2026-09-09. 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. https://arxiv.org/abs/2609.10245

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