{
  "abstract": "We prove a square root bound for the exceptional sets in the binary Goldbach and prime difference problems under quasi Riemann Hypothesis. If every nontrivial zero of every primitive Dirichlet $L$-function has real part at most a fixed $1/2\\leqΘ<11/12$, then $E_+(N)\\ll_ΘN^{1/2}(\\log N)^{100}$ and $E_-(N)\\ll_ΘN^{1/2}(\\log N)^{100}$. Here $E_+(N)$ counts the even integers greater than $2$ and at most $N$ that are not sums of two primes, and $E_-(N)$ counts the positive even integers at most $N$ that are not differences of two primes. The common analytic estimate is a fourth moment bound of the minor arcs for a smoothed prime exponential sum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26756",
  "author_total": 2,
  "authors": [
    {
      "name": "Huixi Li"
    },
    {
      "name": "Zhixin Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d04hetjdntqc2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26756",
  "fulltext_url": null,
  "id": "d04hetjdntqc2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26756",
  "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": "W7223002205",
  "pdf_url": "https://arxiv.org/pdf/2610.26756",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d04hetjdntqc2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26756",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26756"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fourth moments of prime exponential sums and exceptional sets for sums and differences of primes",
  "title_text": "Fourth moments of prime exponential sums and exceptional sets for sums and differences of primes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/d04hetjdntqc2",
  "venue": "arXiv",
  "versions": []
}