{
  "abstract": "We study series $L(x,s):=\\sum_n ρ(n)e^{2πi n x}/n^s$, where $ρ(n)$ are Fourier coefficients of an automorphic form $ϕ$ for a discrete cofinite subgroup $Γ\\subset \\mathrm{SL}(2,\\mathbb{R})$ and $x\\in\\mathbb{R}$. Let $\\mathfrak{b}\\in\\mathbb{R}\\cup\\{\\infty\\}$ represent a cusp of $Γ$. Ordering the orbit $Γ\\mathfrak{b}$ by increasing denominators, we prove that the values $L(x,1/2)$ for $x\\inΓ\\mathfrak{b}$, suitably normalized, become equidistributed according to a standard complex Gaussian law, under natural assumptions on the Laplace eigenvalue of $ϕ$. Previously this was known either when $Γ=\\mathrm{SL}(2,\\mathbb{Z})$ or when $ϕ$ is associated to a holomorphic cusp form. This applies in particular to central values at $s=1/2$ of additive twists of Maass form $L$-functions $\\sum_{n\\geq1}λ(n)e^{2πi n x}/n^s$, or to the Dirichlet-theta series $\\sum_{n\\geq1}χ(n)e^{2πi n^2 x}/n^s$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42008",
  "author_total": 3,
  "authors": [
    {
      "name": "Sandro Bettin"
    },
    {
      "name": "Sandro Bettin"
    },
    {
      "name": "Jungwon Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82skwnksgq8ng.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42008",
  "fulltext_url": null,
  "id": "82skwnksgq8ng",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42008",
  "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/2610.42008",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82skwnksgq8ng.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42008",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42008"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Central values of additive twists of automorphic $L$-series",
  "title_text": "Central values of additive twists of automorphic L-series",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/82skwnksgq8ng",
  "venue": "arXiv",
  "versions": []
}