{
  "abstract": "We present a geometric method for deriving theta function identities from automorphisms of positive definite quadratic forms. Given an automorphism of a quadratic form with matrix $A$, we construct a rational isometry of $I_n\\otimes A$ that fixes the diagonal subspace pointwise. Elementary lattice decompositions and finite character sums then yield explicit transformation formulas for the associated theta functions. As applications, we give a geometric proof of Schultz's generalization of the Borweins' cubic theta identity and recover two related quadratic theta identities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40408",
  "author_total": 1,
  "authors": [
    {
      "name": "Sander Zwegers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bs5akzr09j3z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40408",
  "fulltext_url": null,
  "id": "7bs5akzr09j3z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40408",
  "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/2610.40408",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bs5akzr09j3z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40408",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40408"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Geometric Proofs of Riemann-Type Theta Relations",
  "title_text": "Geometric Proofs of Riemann-Type Theta Relations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/7bs5akzr09j3z",
  "venue": "arXiv",
  "versions": []
}