{
  "abstract": "Let $p$ be a prime, $d\\ge 2$, $H\\in [1,p)$, and $\\ln\\ln p = o(\\ln H)$. We prove that $$ \\min_{1\\le n \\le H} n \\left\\|\\frac{a_1 n}{p}\\right\\|\\ldots \\left\\|\\frac{a_d n}{p}\\right\\| \\approx \\frac{1}{(\\ln p)^{d-1} \\ln H} $$ for \"almost all\" $a \\in ({\\Bbb Z} / p{\\Bbb Z})^d$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08724",
  "author_total": 1,
  "authors": [
    {
      "name": "A. A. Illarionov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7rmgjv2hv0s1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08724",
  "fulltext_url": null,
  "id": "a7rmgjv2hv0s1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08724",
  "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": "W7212067588",
  "pdf_url": "https://arxiv.org/pdf/2609.08724",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7rmgjv2hv0s1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.08724",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08724"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the cardinality of the exception set in Littlewood's discrete conjecture",
  "title_text": "On the cardinality of the exception set in Littlewood's discrete conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/a7rmgjv2hv0s1",
  "venue": "arXiv",
  "versions": []
}