{
  "abstract": "Let $K=\\mathbb{F}_q(θ)$, and let $\\mathcal{Z}$ be the $K$-algebra generated by Thakur's multiple zeta values $ζ_A(\\mathfrak{s})$. We prove that $\\mathcal{Z}$ is a polynomial algebra and construct an explicit polynomial basis of $\\mathcal{Z}$ over $K$. We also determine the transcendence degree of $K[ζ_A(\\mathfrak{s}): \\operatorname{wt}(\\mathfrak{s}) \\leqslant w]$ over $K$ for every integer $w \\geqslant 1$, generalizing a result of Ngo Dac--Nguyen Chu--Pham. The proof uses Chang's grading theorem, the linear basis theorem proved independently by Chang--Chen--Mishiba and Im--Kim--Le--Ngo Dac--Pham, and the carry relations of Im--Kim--Ngo Dac. The key step is to show that suitable derivations obtained from deconcatenation and linear functionals descend through the carry relations to $\\mathcal{Z}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24773",
  "author_total": 1,
  "authors": [
    {
      "name": "Li Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/343desefs4qs7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24773",
  "fulltext_url": null,
  "id": "343desefs4qs7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24773",
  "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|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214049888",
  "pdf_url": "https://arxiv.org/pdf/2609.24773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/343desefs4qs7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A polynomial basis for the multizeta algebra in positive characteristic",
  "title_text": "A polynomial basis for the multizeta algebra in positive characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/343desefs4qs7",
  "venue": "arXiv",
  "versions": []
}