{
  "abstract": "We study sums of Kloosterman sums formed with a modular symbol. Employing Tauberian methods, we first give an estimate for a (Riesz) sum of Ramanujan sums formed with a modular symbol. We further define a zeta function that is analogous to the Selberg zeta function, establish its continuation to $\\Re(s)>1/2$, give estimates for its growth and use this to prove a cancellation statement for sums of these twisted Kloosterman sums. We explain the connection of this construction to the eigenvalue 1/4 problem and formulate an analogue of Linnik's conjecture. Finally, we present numerical evidence that there is cancellation and also that the Kloosterman sums with a modular symbol are not correlated with classical Kloosterman sums.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.10786",
  "author_total": 3,
  "authors": [
    {
      "name": "Nikolaos Diamantis"
    },
    {
      "name": "Solomon Friedberg"
    },
    {
      "name": "Fredrik Strömberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dc8hej10tcztf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10786",
  "fulltext_url": null,
  "id": "dc8hej10tcztf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10786",
  "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": "W7168254522",
  "pdf_url": "https://arxiv.org/pdf/2607.10786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dc8hej10tcztf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2607.10786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Sums of Kloosterman sums formed with modular symbols",
  "title_text": "Sums of Kloosterman sums formed with modular symbols",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dc8hej10tcztf",
  "venue": "arXiv",
  "versions": []
}