{
  "abstract": "We obtain new and essentially optimal bounds on the number of solutions of diagonal systems of $k$ polynomial equations in $s$ variables from an arbitrary finite subset of a finitely generated group in a field of characteristic zero. Our bounds generalise and sometimes improve previous results of J. Bourgain, M. Z. Garaev, S. V. Konyagin, and I. E. Shparlinski (2014), for $k=1$, and of A. Manning, A. Ostafe and I. E. Shparlinski (2026), for $k=2$. In turn, this improvement leads to sharpening a result of A. Manning, A. Ostafe and I. E. Shparlinski (2026) concerning arithmetic statistics of certain matrices. We also obtain similar results for $s$-tuples of linear recurrence sequences, in the case of linear equations and quadratic equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07227",
  "author_total": 3,
  "authors": [
    {
      "name": "Subham Bhakta"
    },
    {
      "name": "Alina Ostafe"
    },
    {
      "name": "Igor E. Shparlinski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkym4k2r6jzgb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07227",
  "fulltext_url": null,
  "id": "fkym4k2r6jzgb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07227",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220964100",
  "pdf_url": "https://arxiv.org/pdf/2610.07227",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkym4k2r6jzgb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07227",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07227"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Systems of equations with elements of finitely generated groups and with linear recurrence sequences",
  "title_text": "Systems of equations with elements of finitely generated groups and with linear recurrence sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/fkym4k2r6jzgb",
  "venue": "arXiv",
  "versions": []
}