{
  "abstract": "We prove Todd's relation conjecture: all $\\mathbb{F}_q(θ)$-linear relations of Thakur's multiple zeta values are generated from the fundamental binary relation by the operators $\\mathcal{B}^{\\mathrm{S}}$, $\\mathcal{C}^{\\mathrm{S}}$, $\\mathcal{B}^{\\mathrm{S}}\\circ \\mathcal{C}^{\\mathrm{S}}$; moreover they are also generated by $\\mathcal{B}^{\\ast\\mathrm{S}}$, $\\mathcal{C}^{\\mathrm{S}}$, $\\mathcal{B}^{\\ast\\mathrm{S}}\\circ\\mathcal{C}^{\\mathrm{S}}$. The $\\mathcal{B}^{\\ast\\mathrm{S}}$-part of this conjecture has been proved by Chang, Chen and Mishiba. We prove the whole conjecture for Carlitz multiple polylogarithm values, which implies the $\\mathcal{B}^{\\mathrm{S}}$-part for multiple zeta values. We also determine all fixed relations and binary relations. Let $\\mathfrak{BR}^{\\mathrm{S}}_w$ be the $\\mathbb{F}_q(θ)$-linear space spanned by binary relations of weight $w$, and let $\\operatorname{Fix}^{\\mathrm{S}}_w$ be the $\\mathbb{F}_q(θ)$-linear space spanned by fixed relations. We derive generating functions $\\sum_{w\\ge 1}\\bigl(\\dim_{\\mathbb{F}_q(θ)}\\operatorname{Fix}^{\\mathrm{S}}_w\\bigr)x^w=\\frac{x^{q+1}(1-x)}{(1-2x)(1-2x+x^{q+1})}$ and $\\sum_{w\\ge 1}\\bigl(\\dim_{\\mathbb{F}_q(θ)}\\mathfrak{BR}^{\\mathrm{S}}_w\\bigr)x^w=\\frac{x^q(1-x)}{(1-2x)(1-2x+x^{q+1})}.$ Our results are based on the recent work of Im-Kim-Ngo Dac on the $\\mathbb{F}_q$-linear relations of Thakur's multiple zeta values, and a system of transfer theorems between multiple zeta values and multiple polylogarithm values.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08263",
  "author_total": 1,
  "authors": [
    {
      "name": "Jinyuan Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aetgr21vyvppg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08263",
  "fulltext_url": null,
  "id": "aetgr21vyvppg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08263",
  "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": "W7212009350",
  "pdf_url": "https://arxiv.org/pdf/2609.08263",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aetgr21vyvppg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.08263",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08263"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Todd's relation conjecture and binary relations for multiple zeta values in positive characteristic",
  "title_text": "Todd's relation conjecture and binary relations for multiple zeta values in positive characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/aetgr21vyvppg",
  "venue": "arXiv",
  "versions": []
}