{
  "abstract": "We previously conjectured a Hecke-type identity for a series arising from two-color partitions. Banerjee and Bringmann proved the conjecture using modular methods and asked for a direct proof using Bailey pairs. They also suggested investigating the odd part of the series. We answer both questions by applying Bailey's transform to a Bailey pair of Andrews and a conjugate Bailey pair of Lovejoy. Our main theorem gives formulas for the even and odd parts of a series $P_a(q)$ depending on a parameter $a$. The specialization $a=1$ gives the conjectured formula and a companion formula for the odd part.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15107",
  "author_total": 2,
  "authors": [
    {
      "name": "George E. Andrews"
    },
    {
      "name": "Mohamed El Bachraoui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54b54375cdpch.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15107",
  "fulltext_url": null,
  "id": "54b54375cdpch",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15107",
  "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|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7161307063",
  "pdf_url": "https://arxiv.org/pdf/2605.15107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54b54375cdpch.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2605.15107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Solutions for Hecke Sum Questions of Banerjee and Bringmann",
  "title_text": "Solutions for Hecke Sum Questions of Banerjee and Bringmann",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/54b54375cdpch",
  "venue": "arXiv",
  "versions": []
}