{
  "abstract": "We establish a uniform effective Chebotarev-Sato-Tate estimate for abelian varieties, conditional on the Mumford-Tate conjecture and the standard analytic conjectures for L-functions attached to the irreducible representations of the Chebotarev-Sato-Tate group. The proof uses spectral majorants and minorants of indicator functions. For regions whose boundaries have finite upper (d-1)-dimensional Minkowski content, the resulting exponent improves that in Bucur et al. (Theorem 1.1, 2024) whenever the Sato-Tate group has rank greater than one. We establish uniform estimates for regions and finite Galois extensions that vary with the counting parameter, and for prime-dependent regions satisfying an explicit variation condition. As an application, we obtain a conditional upper bound for the number of primes at which a weight-two newform with a quadratic coefficient field has a rational Fourier coefficient. We also formulate a discrepancy conjecture, motivated by a probabilistic model, that implies the asymptotic predicted by Murty (Conjecture 3.4, 1999).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36464",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammed Amin Amri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a76572n71yar6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36464",
  "fulltext_url": null,
  "id": "a76572n71yar6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36464",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7224077587",
  "pdf_url": "https://arxiv.org/pdf/2610.36464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a76572n71yar6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Effective Chebotarev-Sato-Tate distribution for Abelian varieties with applications",
  "title_text": "Effective Chebotarev-Sato-Tate distribution for Abelian varieties with applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/a76572n71yar6",
  "venue": "arXiv",
  "versions": []
}