{
  "abstract": "Let $\\mathbb{F}_q$ be a finite field of odd characteristic with $q \\equiv 2 \\pmod3$. We study the directed graph defined by the Borwein--Borwein cubic arithmetic--geometric mean (AGM) over $\\mathbb{F}_q$. We prove that this graph is a disjoint union of directed cycles. We associate Hessian curves with this AGM. We also show that each edge corresponds to a $3$-isogeny defined over $\\mathbb{F}_q$ between the curves associated with its initial and terminal vertices. We then use a counting formula for Hessian curves to derive a lower bound for the number of cycles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14300",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuji Hashimoto"
    },
    {
      "name": "Koji Nuida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4fj843nkqy9f3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14300",
  "fulltext_url": null,
  "id": "4fj843nkqy9f3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14300",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213319844",
  "pdf_url": "https://arxiv.org/pdf/2609.14300",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4fj843nkqy9f3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14300",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14300"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cubic AGM graphs and Hessian $3$-isogenies over finite fields $\\mathbb{F}_q$ of odd characteristic with $q \\equiv 2 \\pmod3$",
  "title_text": "Cubic AGM graphs and Hessian $3$-isogenies over finite fields 𝔽_q of odd characteristic with q ≡ 2 pmod3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4fj843nkqy9f3",
  "venue": "arXiv",
  "versions": []
}