{
  "abstract": "In this paper, for a given Dirichlet character mod $N$ with $4\\nmid N$, we give a lower bound of order $\\sqrt{s/\\log(s)}$ for the dimension of the $\\mathbb{Q}(e^{2i\\pi/N})$-vector space spanned by the values of its $L$-function at integers $\\leq s$ of a given parity. We thus generalize a result Fischler proved in 2021, corresponding to the principal character mod 1. To this end, we construct linear combinations of these values of $L$-function with a refined version of Siegel's lemma, and we apply to them a linear independence criterion generalizing the one used by Fischler. To check the assumptions of this criterion, we rely on a ``Shidlovskii's lemma\".",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2512.02612",
  "author_total": 1,
  "authors": [
    {
      "name": "Ludovic Mistiaen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ff2bwscv41q0f.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "ff2bwscv41q0f",
  "issns": [],
  "landing_url": "https://hal.science/hal-05390882v2",
  "language": "en",
  "licence": "CC-BY-ND-4.0",
  "licence_label": "CC BY-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-nt"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05390882/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ff2bwscv41q0f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05390882",
      "source": "hal",
      "url": "https://hal.science/hal-05390882v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-nt",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Linear independence of values of Dirichlet $L$ functions",
  "title_text": "Linear independence of values of Dirichlet L functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/ff2bwscv41q0f",
  "venue": "HAL",
  "versions": []
}