{
  "abstract": "We provide explicit bounds on the number of zeros for $ζ$ in short intervals near the edge of the critical strip. Ultimately we show that even in short intervals a positive proportion of zeros will not be near the edge of the critical strip. For example with $h>100$ and $t>10^{100}$ the proportion of zeros of $ζ$ with imaginary part in $[t-h,t+h]$ which have real part in $[\\frac{1}{16},\\frac{15}{16}]$ is at least $13\\%$ and a positive proportion is already obtained at $t>10^{43}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22624",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrew Fiori"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5scdw24g8yq4p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22624",
  "fulltext_url": null,
  "id": "5scdw24g8yq4p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22624",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214030784",
  "pdf_url": "https://arxiv.org/pdf/2609.22624",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5scdw24g8yq4p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22624",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22624"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Zero density theorems for short intervals",
  "title_text": "Zero density theorems for short intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/5scdw24g8yq4p",
  "venue": "arXiv",
  "versions": []
}