{
  "abstract": "Let $T \\to \\infty$, let $τ$ be uniformly distributed on $[T,2T]$, and let $σ= σ(T)$ be a deterministic real part approaching $1/2$ from the right. We establish the convergence in law of the recentered maximum of $\\log|ζ(σ+ \\mathrm{i}τ+ \\mathrm{i} h)|$ over $I_θ = \\smash{[ - (\\log T)^θ,(\\log T)^θ]}$, for every fixed $θ> 0$. Under explicit conditions on the displacement $σ- 1/2$, the recentered maximum converges to a Gumbel distribution with scale parameter $1/(2\\sqrt{1 + θ})$. The recentering is an exact upper quantile of the one-point law of the associated Haar field $F_{h}^{\\mathrm{H}} = \\Re\\sum_{p^{j}\\leq X}U_{p}^{j}/(jp^{j(σ+ \\mathrm{i} h)})$, where the $U_{p}$ are independent and uniformly distributed on the complex unit circle. The positive constant in the limiting distribution is characterized by a Gaussian process describing the limiting microscopic increments of the Haar field around a high point. The result is established without the Riemann hypothesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01905",
  "author_total": 1,
  "authors": [
    {
      "name": "Frédéric Ouimet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4e85hbganz70.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01905",
  "fulltext_url": null,
  "id": "d4e85hbganz70",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01905",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01905",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4e85hbganz70.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01905",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01905"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convergence in law of the maximum of the Riemann zeta function on expanding intervals near the critical line",
  "title_text": "Convergence in law of the maximum of the Riemann zeta function on expanding intervals near the critical line",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d4e85hbganz70",
  "venue": "arXiv",
  "versions": []
}