{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10245",
  "author_total": 1,
  "authors": [
    {
      "name": "Brandon Alberts"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f9e0xfn3gqsgn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10245",
  "fulltext_url": null,
  "id": "f9e0xfn3gqsgn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10245",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212116917",
  "pdf_url": "https://arxiv.org/pdf/2609.10245",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f9e0xfn3gqsgn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10245",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10245"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "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",
  "title_text": "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",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/f9e0xfn3gqsgn",
  "venue": "arXiv",
  "versions": []
}