{
  "abstract": "We show that partial sums of the Sato--Tate random multiplicative functions introduced by Cogdell and Michel exhibit better-than-square-root cancellation. The proof proceeds via a connection to multiplicative chaos, following Harper's seminal work. By a non-trivial adaptation of Harper's derandomization argument for character sums, we also obtain upper bounds for low moments of Hecke eigenvalue sums and of Hecke eigenforms near the cusp $0$; to our knowledge, this is the first appearance of multiplicative chaos in the context of automorphic forms on $\\mathrm{GL}(2)$. A novel ingredient is the introduction of Hecke $s$-norms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15937",
  "author_total": 3,
  "authors": [
    {
      "name": "Jad Hamdan"
    },
    {
      "name": "Sun-Kai Leung"
    },
    {
      "name": "Mo Dick Wong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mwyvcqd90j06.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15937",
  "fulltext_url": null,
  "id": "4mwyvcqd90j06",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15937",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.15937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mwyvcqd90j06.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Low moments of Hecke eigenvalue sums",
  "title_text": "Low moments of Hecke eigenvalue sums",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4mwyvcqd90j06",
  "venue": "arXiv",
  "versions": []
}