{
  "abstract": "We prove new large value estimates for the Riemann zeta function on the critical line. For instance, we improve the upper bound on the measure of $t\\in [T, 2T]$ with $|ζ(1/2 + it)| \\geq T^{1/8}$ for the first time since Hardy-Littlewood (1923). Our results imply improved upper bounds on the $k$-th moment of zeta for every $4 < k \\leq 12$. We show in particular that \\begin{equation*} \\int_{0}^{T} |ζ(\\tfrac{1}{2} + it)|^6 \\,d t \\ll_\\varepsilon T^{\\frac{5}{4} - \\frac{1}{60} + \\varepsilon}. \\end{equation*} The main ingredient is a new large value estimate for exponential sums with square-root phases, and certain perturbations. Those arise in the expansion of the short second moment of zeta.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01035",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexandre de Faveri"
    },
    {
      "name": "Mayank Pandey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ammxhcqxacvme.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01035",
  "fulltext_url": null,
  "id": "ammxhcqxacvme",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01035",
  "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": "W7215832989",
  "pdf_url": "https://arxiv.org/pdf/2610.01035",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ammxhcqxacvme.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01035",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01035"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The sixth moment of the Riemann zeta function",
  "title_text": "The sixth moment of the Riemann zeta function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/ammxhcqxacvme",
  "venue": "arXiv",
  "versions": []
}