{
  "abstract": "We study a deformation of the central heat trace on $\\mathrm U(N)$ obtained by deforming Schur polynomials to Jack polynomials, and prove that it admits an asymptotic expansion to arbitrary order. Its coefficients are governed by elliptic $b$-Hurwitz numbers, which are genus-one counterparts of the $b$-Hurwitz theory of Chapuy and Dołęga \\cite{ChapuyDolega22}. We construct the associated elliptic $b$-Hurwitz theory by means of generalized coverings on a torus and identify it with the genus-one closure of the genus-zero simple $b$-Hurwitz theory. At $b=0$ the construction recovers ordinary elliptic Hurwitz theory, while at $b=1$ it gives an automorphism-weighted geometric interpretation of the connected and disconnected twisted elliptic Hurwitz numbers of Hahn--Markwig \\cite{HahnMarkwig26}. Our results extend the topological expansion obtained in the classical case in \\cite{LemMai25,LM2} and take the form of a coupling between chiral and antichiral elliptic $b$-Hurwitz generating functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12256",
  "author_total": 1,
  "authors": [
    {
      "name": "Thibaut Lemoine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/154rj6h8rjh93.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12256",
  "fulltext_url": null,
  "id": "154rj6h8rjh93",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12256",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213069536",
  "pdf_url": "https://arxiv.org/pdf/2609.12256",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/154rj6h8rjh93.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12256",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12256"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Elliptic $b$-Hurwitz theory and Jack heat trace",
  "title_text": "Elliptic b-Hurwitz theory and Jack heat trace",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/154rj6h8rjh93",
  "venue": "arXiv",
  "versions": []
}