{
  "abstract": "We study the algebra of formal finite multiple zeta values by imposing the stuffle and linear shuffle relations of Kaneko and Zagier. Our first results are a surjective homomorphism to the algebra of formal symmetric multiple zeta values and a parity reduction in depth at most four. In even weight we construct a quotient of the formal double zeta space which is isomorphic to the space of formal finite multiple zeta values of depth at most four. The proof combines an explicit depth-three reduction with a motivic lower bound. We also attach to every even period polynomial an explicit relation among the values $ζ_{A}(2a,1,2b,1)$, and these give all relations among the corresponding formal values.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.15480",
  "author_total": 2,
  "authors": [
    {
      "name": "Henrik Bachmann"
    },
    {
      "name": "Risan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7fy5d5eheb1qc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.15480",
  "fulltext_url": null,
  "id": "7fy5d5eheb1qc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.15480",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7203704451",
  "pdf_url": "https://arxiv.org/pdf/2608.15480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7fy5d5eheb1qc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2608.15480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.15480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Formal finite multiple zeta values",
  "title_text": "Formal finite multiple zeta values",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/7fy5d5eheb1qc",
  "venue": "arXiv",
  "versions": []
}