{
  "abstract": "Assuming the Riemann Hypothesis and the simplicity of the non-trivial zeros of the Riemann zeta function $ζ(s)$, we prove lower bounds for the discrete moments $\\sum_{0<γ\\le T}|ζ(2ρ)/ζ'(ρ)|^{2k}$ for every fixed rational $k\\ge1$, and for every fixed real $k\\ge1$. At $k=1$ we give a new proof of the explicit bound, half of the main term conjectured by Ng.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.12376",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrew Pearce-Crump"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x5dj348hwy3g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.12376",
  "fulltext_url": null,
  "id": "5x5dj348hwy3g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.12376",
  "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": "W7164397166",
  "pdf_url": "https://arxiv.org/pdf/2606.12376",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x5dj348hwy3g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2606.12376",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.12376"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lower bounds for discrete moments in a conjecture of Ng",
  "title_text": "Lower bounds for discrete moments in a conjecture of Ng",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/5x5dj348hwy3g",
  "venue": "arXiv",
  "versions": []
}