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PreprintCC BY 4.0arXiv

Inertial multiplicity bounds for two dimensional projective representations and bounds for the number of PSL2(𝔽q) and PGL2(𝔽q) 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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Cite

BibTeXRIS
BibTeX
@misc{alberts2026inertial,
  title = {{Inertial multiplicity bounds for two dimensional projective representations and bounds for the number of $\operatornamePSL_2(\mathbbF_q)$ and $\operatornamePGL_2(\mathbbF_q)$ number fields}},
  author = {Brandon Alberts},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10245},
  eprint = {2609.10245},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10245},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Inertial multiplicity bounds for two dimensional projective representations and bounds for the number of PSL_2(𝔽_q) and PGL_2(𝔽_q) number fields
AU  - Brandon Alberts
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10245
UR  - https://arxiv.org/abs/2609.10245
AB  - 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.
ER  -