{
  "abstract": "We study the contrast between the large-sieve norm and the second moment of structured prime coefficients for sextic residue characters over the Eisenstein integers. For squarefree row and column ideals of norms at most A and B, we prove a lower bound of order (AB)^(-epsilon) times (A + B + A^(5/6) B^(1/3) + A^(1/3) B^(5/6)), matching de Faveri's upper bound throughout the full parameter range. In particular, the squared full-cutoff norm at balance is at least Q^(7/6 - epsilon). The proof uses the uniform unmarked character moments of OpenAI's September 2026 manuscript, a Gauss second moment uniform in moving prime exclusions, and a centered comparison that transports a squarefree-row signal between column scales. With the additional unmarked inverse moment and buffered zero detector from the same source, we derive a low-height zero-density estimate and bound the second moment of a fixed smooth prime sum by Q^((37 - 10 sqrt(6))/6 + epsilon). We also treat bounded convolutions of independently weighted large primes. An appendix retains the first version's unbalanced lower bound and its exponent 17/16, without using the additional plain or inverse moment estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17675",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuanda Xu"
    },
    {
      "name": "Hejian Sang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6t3rbhwmvpdn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17675",
  "fulltext_url": null,
  "id": "6t3rbhwmvpdn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17675",
  "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": "W7221773708",
  "pdf_url": "https://arxiv.org/pdf/2610.17675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6t3rbhwmvpdn9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.17675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17675"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A matching lower bound for the sextic large sieve and structured prime moments",
  "title_text": "A matching lower bound for the sextic large sieve and structured prime moments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/6t3rbhwmvpdn9",
  "venue": "arXiv",
  "versions": []
}