{
  "abstract": "We investigate the Hasse principle for systems consisting of one form of degree $k$ which decomposes as a sum of $n$-ary forms, and one general form of degree $d < k$. By exploiting the block structure of the first form before applying Weyl differencing, we refine the method of Brandes and Parsell (arXiv:2003.04350) in this setting; in particular, for a sum of binary quartic forms and a quadratic form, the requirement $s > 516$ is relaxed to $s > 96$, which also improves on the bound $s > 100$ available for general forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35639",
  "author_total": 1,
  "authors": [
    {
      "name": "Anna Theorin Johansson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9d1rjk3rkn12n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35639",
  "fulltext_url": null,
  "id": "9d1rjk3rkn12n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35639",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223956736",
  "pdf_url": "https://arxiv.org/pdf/2610.35639",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9d1rjk3rkn12n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35639",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35639"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Hasse principle for a block-diagonal form and a form of lower degree",
  "title_text": "On the Hasse principle for a block-diagonal form and a form of lower degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9d1rjk3rkn12n",
  "venue": "arXiv",
  "versions": []
}