{
  "abstract": "This paper broadens the range on which Fouvry and Radziwiłł's results on nearly balanced convolutions apply. In particular, let $α_m$ and $β_n$ be sequences supported on $m\\sim M$ and $n\\sim N$ where $β_n$ is equidistributed for small moduli, and let $Q=X^{\\frac 12+\\varepsilon}$. We find that \\begin{gather*}\\sum_{q\\sim Q}\\left|\\mathop{\\sum\\sum}_{\\substack{n\\sim N,m\\sim M \\\\ mn\\equiv a\\pmod q}}α_mβ_n-\\frac{1}{ϕ(q)}\\mathop{\\sum\\sum}_{\\substack{n\\sim N,m\\sim M \\\\ (mn,q)=1}}α_mβ_n\\right|\\ll \\frac{X}{\\log^A X} \\end{gather*} if $N=X^{\\frac 12+δ}$ and $M=X^{\\frac 12-δ}$ with $0<δ<\\frac 1{68}$, which improves Fouvry and Radziwiłł's $0<δ<\\frac 1{112}$. To prove this, we sharpen Bettin and Chandee's famous result on trilinear forms with Kloosterman fractions in the case where some of the sums are over subdyadic intervals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27732",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Wright"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42mttshkc1g7z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27732",
  "fulltext_url": null,
  "id": "42mttshkc1g7z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27732",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7204851823",
  "pdf_url": "https://arxiv.org/pdf/2608.27732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42mttshkc1g7z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions",
  "title_text": "Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/42mttshkc1g7z",
  "venue": "arXiv",
  "versions": []
}