{
  "abstract": "Bringmann, Han, Heim, and Kane recently investigated periodic sign patterns in the Fourier coefficients of weakly holomorphic modular forms arising from eta-quotients and posed numerous conjectures in the appendix to their work. Using classical theta-function identities, dissections, and coefficientwise positivity, we prove 72 of these conjectural sign patterns. The eta-quotients considered here have periods 2, 3, 4, 5, 6, 8, and 12. Our proofs are elementary at the level of $q$-series and yield explicit generating functions for the coefficients in each relevant residue class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35893",
  "author_total": 3,
  "authors": [
    {
      "name": "Jing Jin"
    },
    {
      "name": "Olivia X. M. Yao"
    },
    {
      "name": "Shiwen Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0yf5bt898jzmm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35893",
  "fulltext_url": null,
  "id": "0yf5bt898jzmm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35893",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214988096",
  "pdf_url": "https://arxiv.org/pdf/2609.35893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0yf5bt898jzmm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.35893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Proofs of some conjectures by Bringmann, Han, Heim, and Kane on periodic sign changes in eta-quotients",
  "title_text": "Proofs of some conjectures by Bringmann, Han, Heim, and Kane on periodic sign changes in eta-quotients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/0yf5bt898jzmm",
  "venue": "arXiv",
  "versions": []
}