{
  "abstract": "In 1985 Kohnen used the Shimura correspondence to prove a general formula relating the coefficients of half-integral weight modular forms of level $ 4N $ transforming with respect to the theta multiplier to central values of $ L $-functions for twists of newforms of level $ N $. This generalized previous work with Zagier. In this paper, we prove a Kohnen-Zagier type formula using Yang's Shimura correspondence for powers of the eta multiplier in level $ 1 $, relating the coefficients of half-integral weight modular forms to central values of $ L $-functions for twists of newforms of level $ 6 $. To do so we develop some of the theory of modular forms transforming with respect to powers of the eta multiplier and introduce Shintani lifts of level $ 6 $, with Fourier coefficients given in terms of cycle integrals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38051",
  "author_total": 1,
  "authors": [
    {
      "name": "Clayton Williams"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/azb0mhdke0d6t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38051",
  "fulltext_url": null,
  "id": "azb0mhdke0d6t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38051",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38051",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/azb0mhdke0d6t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38051",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38051"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Kohnen-Zagier Formula in Level 1",
  "title_text": "A Kohnen-Zagier Formula in Level 1",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/azb0mhdke0d6t",
  "venue": "arXiv",
  "versions": []
}