{
  "abstract": "We study Fourier coefficients of the Siegel-Eisenstein series $E_{m+1}^{(2m)}(Z)$ for $m\\equiv1\\pmod4$ and $m\\geq5$. Using the Fourier expansion formula due to Mizumoto, we determine the constant term and the exceptional non-zero Fourier coefficients. The result gives a higher-degree analogue of the degree-two formulas of Kohnen and Nagaoka, which were later rederived by Haruki.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Ramanujan J. 71, 37 (2026)",
  "arxiv": "2606.09136",
  "author_total": 1,
  "authors": [
    {
      "name": "Nobuki Takeda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91mc2j8xrzb7m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.09136",
  "fulltext_url": null,
  "id": "91mc2j8xrzb7m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.09136",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2606.09136",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91mc2j8xrzb7m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2606.09136",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.09136"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fourier Coefficients of Siegel-Eisenstein Series of Degree $2m$ and Weight $m+1$",
  "title_text": "Fourier Coefficients of Siegel-Eisenstein Series of Degree 2m and Weight m+1",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/91mc2j8xrzb7m",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s11139-026-01490-7",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}