{
  "id": "2212.00366",
  "version": "v1",
  "published": "2022-12-01T08:50:11.000Z",
  "updated": "2022-12-01T08:50:11.000Z",
  "title": "On linear independence of Dirichlet $L$ values",
  "authors": [
    "Sanoli Gun",
    "Neelam Kandhil",
    "Patrice Philippon"
  ],
  "comment": "20 pages",
  "journal": "Journal of Number Theory, vol. 244, 2023, 63-83",
  "doi": "10.1016/j.jnt.2022.09.016",
  "categories": [
    "math.NT"
  ],
  "abstract": "The study of linear independence of $L(k, \\chi)$ for a fixed integer $k>1$ and varying $\\chi$ depends critically on the parity of $k$ vis-\\`a-vis $\\chi$. This has been investigated by a number of authors for Dirichlet characters $\\chi$ of a fixed modulus and having the same parity as $k$.The focal point of this article is to extend this investigation to families of Dirichlet characters modulo distinct pairwise co-prime natural numbers. The interplay between the resulting ambient number fields brings in new technical issues and complications hitherto absent in the context of a fixed modulus (consequently a single number field lurking in the background). This entails a very careful and hands-on dealing with the arithmetic of compositum of number fields which we undertake in this work. Our results extend earlier works of the first author with Murty-Rath as well as works of Okada, Murty-Saradha and Hamahata.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-01T08:50:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11R18",
      "11M06"
    ],
    "keywords": [
      "linear independence",
      "ambient number fields brings",
      "dirichlet characters modulo distinct",
      "characters modulo distinct pairwise co-prime",
      "distinct pairwise co-prime natural numbers"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}