{
  "abstract": "Let \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\boldsymbol{x})$$\\end{document}f(x) be a non-singular quadratic form with sufficiently many mixed terms and t an integer. For a sequence of weights \\mathcal AA we study the number of weighted solutions to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\boldsymbol{x}) = t$$\\end{document}f(x)=t. In particular, we give conditions on both \\mathcal AA and f such that we can use the circle method to count such solutions of bounded height.",
  "abstract_shown": true,
  "affiliations": [
    "Inria Saclay, 1 Rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France",
    "École Polytechnique Fédérale de Lausanne/MATH/TAN, Station 8, CH-1015 Lausanne, Switzerland"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mieke Wessel",
      "orcid": "0009-0001-9004-153X"
    },
    {
      "affs": [
        1
      ],
      "name": "Svenja zur Verth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qkp7pwh8x4a9.bib",
  "cited_by": 0,
  "doi": "10.1007/s00605-026-02189-z",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13736505/",
  "id": "6qkp7pwh8x4a9",
  "issns": [
    "0026-9255",
    "1436-5081"
  ],
  "landing_url": "https://doi.org/10.1007/s00605-026-02189-z",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Article"
    ]
  ],
  "openalex": null,
  "pdf_url": null,
  "pmcid": "PMC13736505",
  "pmid": "42991135",
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qkp7pwh8x4a9.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:56Z",
      "native_id": "PMC13736505",
      "source": "pmc",
      "url": "https://doi.org/10.1007/s00605-026-02189-z"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "Solving quadratic forms in restricted variables with the circle method",
  "title_text": "Solving quadratic forms in restricted variables with the circle method",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T12:21:56Z",
  "url": "https://research.draconitic.com/paper/6qkp7pwh8x4a9",
  "venue": "Monatshefte Fur Mathematik",
  "versions": []
}