{
  "abstract": "In this article, we study the mixed-moment problem for the product of central values of two $L$-functions twisted by a Dirichlet character of large conductor $q$. Precisely, for a fixed $\\mathrm{SL}_3(\\mathbb{Z})$ Hecke-Maass cusp form $π$, we asymptotically evaluate the first moment, with $\\textit{power-saving}$ error term for the product of central $L$-values $L(1/2, π\\timesχ)\\overline{L(1/2, χ)}$ averaged over the $\\textit{full family}$ $\\{χ\\,(\\mathrm{mod}\\,{q}): Q\\leq q\\leq 2Q\\}$ of primitive Dirichlet characters modulo $q$. And as a consequence, we also established the simultaneous non-vanishing of the aforementioned central $L$-values.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20792",
  "author_total": 2,
  "authors": [
    {
      "name": "Sayan Ghosh"
    },
    {
      "name": "Pratim Mitra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50egs3ff0hct5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20792",
  "fulltext_url": null,
  "id": "50egs3ff0hct5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20792",
  "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|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7222722979",
  "pdf_url": "https://arxiv.org/pdf/2610.20792",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50egs3ff0hct5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.20792",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20792"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Mixed moment and joint non-vanishing of $\\mathrm{GL}(3)\\times\\mathrm{GL}(1)$ and $\\mathrm{GL}(1)$ $L$-functions",
  "title_text": "Mixed moment and joint non-vanishing of GL(3)×GL(1) and GL(1) L-functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/50egs3ff0hct5",
  "venue": "arXiv",
  "versions": []
}