{
  "abstract": "We prove the expected asymptotic in Waring's problem over $\\mathbb F_q[T]$, with a power-saving error, whenever $n>2d$, the characteristic is greater than $(d-1)^2$, and $q$ satisfies an explicit lower bound. This range is sharp in general for the expected asymptotic uniformly in the target polynomial. Our main new input is an aggregate minor arc estimate: we count functionals according to the codimension of their associated singular loci and use intersection theory to bound the degrees of the resulting parameter spaces. In particular, if $n\\ge (2+\\varepsilon)d$, the required lower bound on $q$ is polynomial in $d$ of degree $2+4/\\varepsilon$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11888",
  "author_total": 1,
  "authors": [
    {
      "name": "Matthew Hase-Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95ad5t9edqf5f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11888",
  "fulltext_url": null,
  "id": "95ad5t9edqf5f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11888",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7212285298",
  "pdf_url": "https://arxiv.org/pdf/2609.11888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95ad5t9edqf5f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11888"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The asymptotic in Waring's problem over function fields beyond twice the degree",
  "title_text": "The asymptotic in Waring's problem over function fields beyond twice the degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/95ad5t9edqf5f",
  "venue": "arXiv",
  "versions": []
}