{
  "abstract": "An old conjecture dating back at least to Hildebrand's work in 1989, asserts that the M\\\"obius function exhibits cancellation on shifted primes; that is, $$\\sum_{p\\le x}\\mu(p+h)=o\\big(\\pi(x)\\big)$$ for any fixed shift $h>0$. This is also a well-known model case for the parity problem in sieve theory. In this paper, we prove this conjecture. As an application, we show that each of the values $1$ and $-1$ of $\\mu(p+h)$ occur with asymptotic density $1/2$: \\begin{equation*} \\lim_{x\\to\\infty} \\frac{\\#\\{p\\le x:\\ \\mu(p+h)=\\kappa\\}} {\\#\\{p\\le x:\\ \\mu^2(p+h)=1\\}} =\\frac12, \\quad \\kappa\\in\\{-1,1\\}. \\end{equation*}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20242",
  "author_total": 3,
  "authors": [
    {
      "name": "Guangshi Lü"
    },
    {
      "name": "Zhiwei Wang"
    },
    {
      "name": "Jie Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6rp6q19a5vw3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20242",
  "fulltext_url": null,
  "id": "f6rp6q19a5vw3",
  "issns": [],
  "landing_url": "https://hal.science/hal-05793028v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-nt"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221929628",
  "pdf_url": "https://hal.science/hal-05793028/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6rp6q19a5vw3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "hal-05793028",
      "source": "hal",
      "url": "https://hal.science/hal-05793028v1"
    },
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Hardy--Littlewood--Chowla conjecture",
  "title_text": "On the Hardy--Littlewood--Chowla conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/f6rp6q19a5vw3",
  "venue": "HAL",
  "versions": []
}