{
  "abstract": "Let $f$ be a primitive holomorphic cusp form of arbitrary weight, level and nebentypus. We prove $\\int_0^T|L(1/2+it,f)|^6\\,dt\\ll_{f,ε}T^{2+ε}$, extending Jutila's level-one theorem. The new ingredient is a large sieve comparing the stationary phases in the Booker-Milinovich-Ng transformation at different heights. Applications include moments of order $T^{1+ε}$ on every line to the right of the critical line, $Ω(T^{4/35-ε})$ simple zeros, zero density estimates, and bounds for cubic-field power sums, shifted convolution sums and the general divisor problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39706",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrew Pearce-Crump"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3420sj98f49de.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39706",
  "fulltext_url": null,
  "id": "3420sj98f49de",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39706",
  "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|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7215046239",
  "pdf_url": "https://arxiv.org/pdf/2609.39706",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3420sj98f49de.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2609.39706",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39706"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The sixth moment of a degree two $L$-function of arbitrary level",
  "title_text": "The sixth moment of a degree two L-function of arbitrary level",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/3420sj98f49de",
  "venue": "arXiv",
  "versions": []
}