{
  "abstract": "We study the distribution and oscillatory properties of prime-supported Fourier coefficients attached to a Hecke--Maass form for $\\mathrm{SL}(3, \\mathbb{Z})$ twisted by additive characters. For linear phases involving irrationals of finite type, we construct an automorphic variant of Vaughan's identity and exploit bilinear cancellation to obtain an unconditional power-saving estimate. For non-linear phases $e(αn^θ)$ with $0 < θ< 1$, we refine the Type~II bilinear forms via Weyl differencing and modern exponent pair methods. Combined with the analysis of untwisted $\\mathrm{GL}(3)$ sums, this framework breaks the $2/3$-barrier of Jiang and Lü and widens the admissible range of non-trivial cancellation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18928",
  "author_total": 1,
  "authors": [
    {
      "name": "K. Venkatasubbareddy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jgd1f4p90vhz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18928",
  "fulltext_url": null,
  "id": "7jgd1f4p90vhz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18928",
  "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": "W7221871358",
  "pdf_url": "https://arxiv.org/pdf/2610.18928",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jgd1f4p90vhz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.18928",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18928"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Orthogonality relation between $GL(3)$ coefficients and additive characters with linear and non-linear phases",
  "title_text": "Orthogonality relation between GL(3) coefficients and additive characters with linear and non-linear phases",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/7jgd1f4p90vhz",
  "venue": "arXiv",
  "versions": []
}