{
  "abstract": "We compute the Fourier expansions of the Kudla-Millson theta lifts of vector-valued Hilbert cusp forms of parallel weight. These expansions are with respect to 0-dimensional cusps of non-compact orthogonal Shimura varieties defined over any totally real number field, and computed using a mixed model of the adelic Weil representation under a partial Fourier transform. As a consequence, we obtain the injectivity of the theta lifts under some additional hypothesis on the variety. Furthermore, we show that the theta lifts are square-integrable harmonic differential forms, and deduce lower bounds for dimensions of cohomology groups of such varieties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12148",
  "author_total": 3,
  "authors": [
    {
      "name": "Yingkun Li"
    },
    {
      "name": "Mingkuan Zhang"
    },
    {
      "name": "Riccardo Zuffetti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0b6nehskhjj9c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12148",
  "fulltext_url": null,
  "id": "0b6nehskhjj9c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12148",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212520426",
  "pdf_url": "https://arxiv.org/pdf/2609.12148",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0b6nehskhjj9c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12148",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12148"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An adelic approach to the Kudla-Millson lifts over totally real number fields",
  "title_text": "An adelic approach to the Kudla-Millson lifts over totally real number fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/0b6nehskhjj9c",
  "venue": "arXiv",
  "versions": []
}