{
  "abstract": "We show that the norm of the partial sum operator $S_N$ on the Hardy space $\\mathscr H^1$ of Dirichlet series satisfies $$\\liminf_{N\\to\\infty}\\frac{\\log\\log N}{\\log N}\\lVert S_N\\rVert_{\\mathscr H^1\\to\\mathscr H^1}\\geq\\frac{1-\\log 2}{2π}.$$ Combined with an upper bound of Bondarenko, Brevig, Saksman and Seip, this shows that $$\\lVert S_N\\rVert_{\\mathscr H^1\\to\\mathscr H^1}\\asymp\\frac{\\log N}{\\log\\log N}$$ as $N\\to\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23666",
  "author_total": 1,
  "authors": [
    {
      "name": "Viktor Andersson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3s3a7m8ww9gbz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23666",
  "fulltext_url": null,
  "id": "3s3a7m8ww9gbz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23666",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7222984159",
  "pdf_url": "https://arxiv.org/pdf/2610.23666",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3s3a7m8ww9gbz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23666",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23666"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the asymptotic growth of the norm of the partial sum operator on $\\mathscr H^1$",
  "title_text": "On the asymptotic growth of the norm of the partial sum operator on ℋ^1",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/3s3a7m8ww9gbz",
  "venue": "arXiv",
  "versions": []
}