{
  "abstract": "Version 6, 2026-08-31. This version adds links to the companion interactive web pages (English/Chinese expository sites) and the GitHub code repository. No mathematical content changes from v5. We prove the Generalized Riemann Hypothesis (GRH) for all non-principal Dirichlet L-functions L(s,chi) with conductor q >= 3. The proof proceeds by combining the three-term polylogarithm decomposition of the Riemann zeta function with the completed L-function Lambda(s,chi) to form a product xi_K(s) = xi(s) * Lambda(s,chi). We then establish angular monotonicity of xi_K in polar coordinates centered at s = 1/2, which forces all zeros of xi_K (and hence all zeros of L(s,chi)) to lie on the critical line Re(s) = 1/2. The key ingredient is the non-negativity of the coefficients c_n = 1 - z_1^n - z_2^n, where z_1 = tan(pi/8), z_2 = 1 - tan(pi/8), which follows from elementary inequalities without assuming GRH. This establishes a direct bridge between the arithmetic positivity of the Dirichlet coefficients and the analytic monotonicity required for the zero-free region.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Zhuo Chen",
      "orcid": "0009-0006-9172-8268"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3668sx057hec1.bib",
  "cited_by": 5,
  "doi": "10.5281/zenodo.22137207",
  "fulltext_url": null,
  "id": "3668sx057hec1",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.22137207",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7204571040",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/3668sx057hec1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7204571040",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.22137207"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Analytic Number Theory Research",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Angular Monotonicity of Completed Dirichlet L-Functions via the Three-Term Zeta Decomposition: A Proof of the Generalized Riemann Hypothesis for Non-Principal Characters",
  "title_text": "Angular Monotonicity of Completed Dirichlet L-Functions via the Three-Term Zeta Decomposition: A Proof of the Generalized Riemann Hypothesis for Non-Principal Characters",
  "type": "preprint",
  "updated_at": "2026-11-04T13:21:00Z",
  "url": "https://research.draconitic.com/paper/3668sx057hec1",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}