{
  "abstract": "We develop a new method which allows us to estimate, with a power saving, sums of the M{ö}bius function over function fields ${\\mathbb F}_p(X)$. The sums run over monic polynomials with all other coefficients in short intervals, of length below the Pólya--Vinogradov threshold $p^{1/2}$. A classical result of L. Stickelberger (1898) reduces this question to bounding character sums with polynomial discriminants which are inhomogeneous multivariate polynomials. Variants of Burgess's method with non-linear shifts {\\it {à} la carte} are introduced to go beyond the Pólya--Vinogradov range, combined with a stratification result of J. Xu (2020) for complete character sums.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28822",
  "author_total": 3,
  "authors": [
    {
      "name": "Etienne Fouvry"
    },
    {
      "name": "Igor E. Shparlinski"
    },
    {
      "name": "Ping Xi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etdbdzz7pe5p8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28822",
  "fulltext_url": null,
  "id": "etdbdzz7pe5p8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28822",
  "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": "W7223206587",
  "pdf_url": "https://arxiv.org/pdf/2610.28822",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etdbdzz7pe5p8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.28822",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28822"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Short sums of the Möbius function over function fields",
  "title_text": "Short sums of the Möbius function over function fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/etdbdzz7pe5p8",
  "venue": "arXiv",
  "versions": []
}