{
  "abstract": "We deduce zero-density estimates in short vertical strips from short-interval moments of globally tempered automorphic $L$-functions, by adapting the large-value estimate of Guth and Maynard and the Type II zero argument of Maynard and Pratt to the framework of Ye and Zhang. For the Riemann zeta function, we obtain $N_ζ(σ;T,T+T^a)\\ll T^{15a(1-σ)/(3+5σ)+\\varepsilon}$ for $2/3\\le a\\le1$ and $7/10\\leσ\\le4/5$, improving Ye--Zhang's exponent in the interior of this range. Combining the localized density bound with the recent quasi-Riemann theorems, we estimate smoothed prime-power sums with phase $\\exp(2πiαn^β)$ on intervals of length $K^δ$. For $0<β<13/20$, we obtain a power saving whenever $\\max\\{17/30,1-β\\}<δ<1$; in particular the square-root phase admits every $δ>17/30$. A revised transform estimate retains both the stationary spread and the Fourier width $K/L$. For example, the bound at $β=1/2$, $δ=3/5$ is $K^{15/26+\\varepsilon}$, uniformly for frequencies $mα$ with $1\\le m\\le K^{1/10}$. We also retain power savings for certain self-dual $GL(2)$ twists and self-dual $GL(3)$ cusp forms, without assuming Ramanujan. All three applications have explicit frequency dependence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15989",
  "author_total": 1,
  "authors": [
    {
      "name": "Yangbo Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vn3d91n7gctk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15989",
  "fulltext_url": null,
  "id": "2vn3d91n7gctk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15989",
  "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": "W7221832716",
  "pdf_url": "https://arxiv.org/pdf/2610.15989",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vn3d91n7gctk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.15989",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15989"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Zero density in short strips and short-interval bounds toward Hypothesis S",
  "title_text": "Zero density in short strips and short-interval bounds toward Hypothesis S",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/2vn3d91n7gctk",
  "venue": "arXiv",
  "versions": []
}