{
  "abstract": "In this paper, we establish an asymptotic formula of mixed moments of $L(1/2,f)$ and $L(1/2,\\mathrm{sym}^2 f)$ for cusp forms $f$ of weight $k$, prime level $q$ and real primitive nebentypus $χ$ modulo $q$ in the level aspect with a power-saving error term. As an application, we deduce the simultaneous non-vanishing of $L(1/2, f)$ and $L(1/2,\\mathrm{sym}^2 f)$ for sufficiently large prime levels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16893",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhiwei Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9yy3vzr67n7g7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16893",
  "fulltext_url": null,
  "id": "9yy3vzr67n7g7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16893",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.16893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9yy3vzr67n7g7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions in the level aspect",
  "title_text": "Mixed moment of GL(2) and GL(3) L-functions in the level aspect",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/9yy3vzr67n7g7",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1090/proc/17898",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}