{
  "abstract": "In this paper we further examine the structure of the graded paramodular Hecke algebra $\\mathcal H$. We define a commutative subring $\\mathcal{H}^α$ of $\\mathcal{H}$ as the elements fixed by a certain automorphism $α$, and we show that the elements $T(q^k)$, defined as the sum of the double cosets of degree $k$, are contained in $\\mathcal{H}^α$. We prove that the formal power series in the indeterminate $t$ with coefficients $T(q^k)$ is an explicit rational function in $t$ with coefficients from $\\mathcal{H}^α$. We also determine the structure of $\\mathcal{H}^α$ and its relation to $\\mathcal{H}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07520",
  "author_total": 3,
  "authors": [
    {
      "name": "Jennifer Johnson-Leung"
    },
    {
      "name": "Joshua Parker"
    },
    {
      "name": "Brooks Roberts"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5m1h5h6p5yfeb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07520",
  "fulltext_url": null,
  "id": "5m1h5h6p5yfeb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07520",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221038699",
  "pdf_url": "https://arxiv.org/pdf/2610.07520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5m1h5h6p5yfeb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Further results on the paramodular Hecke algebra",
  "title_text": "Further results on the paramodular Hecke algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/5m1h5h6p5yfeb",
  "venue": "arXiv",
  "versions": []
}