PAPER / 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

RESUMO

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.

NO MESMO MAPA

Papers relacionados

math.NT18 de set. de 2026

Asymptotic counting of integers with prime factors $p_{r^a s^b}$

Mehdi Golafshan

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

Papers relacionados

Asymptotic counting of integers with prime factors $p_{r^a s^b}$

A uniform proof approach for congruences modulo 3 for partitions with $k$-colored odd parts

Sumsets of Ahlfors--David regular sets

On the Hiraga-Ichino-Ikeda conjecture on formal degrees for $\mathrm{G}_2$

Endoscopic description of the local Langlands correspondence for $\mathrm{G}_2$

A new family of maximal curves not covered by the Hermitian curve