{
  "abstract": "We introduce a new approach to studying correlations between arithmetic functions and linear phases with respect to highly irrational frequencies over short intervals. As an application, we prove that \\[ \\Big|\\sum_{x<n \\leq x+H}μ(n) e(nα)\\Big| \\ll H(\\log x)^{-1/3+\\varepsilon } \\] whenever $x^{0.58+\\varepsilon }\\leq H\\leq x$. In the same range of $H$ we also show that \\[ \\Big|\\sum_{x<n \\leq x+H} Λ(n) e(nα)\\Big| \\ll H(\\log x)^{-A} \\] for arbitrarily large $A>0$ unless there exists an integer $1\\leq q\\ll (\\log x)^{O_A(1)}$ such that $\\|qα\\| \\ll x (\\log x)^{O_A(1)}/H^2$. This breaks the $3/5$ barrier in Theorem 1.5 of arXiv:1911.09076v2 and Theorem 2 of [T. Zhan, \"On the representation of large odd integer as a sum of three almost equal primes,\" Acta Mathematica Sinica 7.3 (1991), 259-272]. Moreover, by our method, any improvement in large value estimates for character-twisted Dirichlet polynomials on the critical range would lead to a corresponding improvement in the lower bound for $H$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11487",
  "author_total": 2,
  "authors": [
    {
      "name": "Javier Pliego"
    },
    {
      "name": "Mengdi Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8w14bwvfmaj6m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11487",
  "fulltext_url": null,
  "id": "8w14bwvfmaj6m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11487",
  "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": "W7221176578",
  "pdf_url": "https://arxiv.org/pdf/2610.11487",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8w14bwvfmaj6m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.11487",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11487"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Discorrelation of the Möbius function with linear phases in short intervals",
  "title_text": "Discorrelation of the Möbius function with linear phases in short intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/8w14bwvfmaj6m",
  "venue": "arXiv",
  "versions": []
}