{
  "abstract": "A decade ago, locally harmonic Maaß forms were first established by Bringmann, Kane, and Kohnen in negative weights and independently by Hövel in weight $0$. Since then, they have seen important applications related to twisted central $L$-values of newforms. However, there are just a few examples of these forms known so far, and in particular there is no unifying theory behind these examples. Towards this direction, we show that the representations of Zagier's $f_{k,D}$ and Mono's $g_{k+1,D}$ functions as traces of cycle integrals are not unique.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.24373",
  "author_total": 1,
  "authors": [
    {
      "name": "Johann Stumpenhusen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8cn2rwgyze2n3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.24373",
  "fulltext_url": null,
  "id": "8cn2rwgyze2n3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.24373",
  "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": "W7204500039",
  "pdf_url": "https://arxiv.org/pdf/2608.24373",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8cn2rwgyze2n3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.24373",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.24373"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals",
  "title_text": "Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/8cn2rwgyze2n3",
  "venue": "arXiv",
  "versions": []
}