{
  "abstract": "Let $g$ be a fixed primitive Hecke--Maass cusp form, and let $f$ vary with spectral parameter $k_f=K$, at a fixed level and with trivial nebentypus. We study smooth sums of $λ_f(n)λ_g(n)e(αn^β)$ for fixed real $α\\ne0$. The crucial input is the smooth spectral second moment of Lau, Liu, and Ye, for which the window length can be taken to be $L=K^{1/3+a}$ for arbitrarily small fixed $a>0$. We show that, for every $κ>0$, there is $β_0>0$ such that the sum is $O(K^{2/3+κ}X^{1/2})$ for $1\\le X\\le K^2$ and $0<β\\leβ_0$. We give a detailed Baire category argument which makes the dependence on the smooth weight uniform through one finite derivative norm. A second argument keeps the phase explicit, applies Voronoi summation and shifted convolution estimates, and gives the numerical bound $O(K^{423/224+(5/7)β+\\varepsilon})$ at $X=K^2$ for $0<β<5/32$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15979",
  "author_total": 1,
  "authors": [
    {
      "name": "Yangbo Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3yd9danq733sr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15979",
  "fulltext_url": null,
  "id": "3yd9danq733sr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15979",
  "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": "W7221776444",
  "pdf_url": "https://arxiv.org/pdf/2610.15979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3yd9danq733sr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nonlinear twists of Rankin-Selberg coefficients in the eigenvalue aspect",
  "title_text": "Nonlinear twists of Rankin-Selberg coefficients in the eigenvalue aspect",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3yd9danq733sr",
  "venue": "arXiv",
  "versions": []
}