{
  "abstract": "A qKZ-type additive discrete flat connection in characteristic $p$ has $p$-curvature operators. They are commuting automorphisms of the connection. We present a Bethe-ansatz-type construction of eigensections and eigenvalues of the $p$-curvature operators. An eigensection of $p$-curvature operators is a discrete hypergeometric sum over the finite lattice $\\mathbb{Z}^r/p\\mathbb{Z}^r$. Thus, the $p$-curvature eigensections are constructed by a finite, discrete analogue of a hypergeometric integral.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21090",
  "author_total": 2,
  "authors": [
    {
      "name": "Vitaly Tarasov"
    },
    {
      "name": "Alexander Varchenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44tkvq2dx7ewv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21090",
  "fulltext_url": null,
  "id": "44tkvq2dx7ewv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21090",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213945701",
  "pdf_url": "https://arxiv.org/pdf/2609.21090",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44tkvq2dx7ewv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2609.21090",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21090"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Eigenvectors of $p$-Curvature for Geometric Difference Equations",
  "title_text": "Eigenvectors of p-Curvature for Geometric Difference Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/44tkvq2dx7ewv",
  "venue": "arXiv",
  "versions": []
}