{
  "abstract": "We refine the ordinary product moment in the cubic-theta comparison by allowing a returned prime product to be exhausted. The return stops either when the positive-prime length inequality holds or when the established prime-free ordinary estimate applies. Keeping the extracted central coefficients gives a local normalization inequality on a larger domain. On the critical ordinary-length interval this yields a net first-mean gain of $1/20000$. We prove the complementary-class, short-sum and algebraic comparison inequalities directly, and obtain the endpoint $B_*-1/160000=0.87446205769353\\ldots$, where $B_*$ is Liu's algebraic boundary. The zero-free conclusion is conditional on the cited general-field theta, detector, prior-bound and Mellin input theorems in their stated uniform forms. The proof includes the actual return weights, both approximate-functional-equation arms, the principal-residue normalization and descent to arbitrary number fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00924",
  "author_total": 2,
  "authors": [
    {
      "name": "Xinrui Chang"
    },
    {
      "name": "HaoMing Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8htkqdp1fnj64.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00924",
  "fulltext_url": null,
  "id": "8htkqdp1fnj64",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00924",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00924",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8htkqdp1fnj64.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00924",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00924"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An exhaustion-aware product moment and zero-free half-planes for Hecke L-functions",
  "title_text": "An exhaustion-aware product moment and zero-free half-planes for Hecke L-functions",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8htkqdp1fnj64",
  "venue": "arXiv",
  "versions": []
}