{
  "abstract": "For a finite set $S$ of positive integers, put $K(S):=-\\min_{x\\in\\mathbb T}\\sum_{s\\in S}\\cos(2πsx)$. Bedert recently proved the uniform lower bound $K(S)\\geq |S|^{1/5-o(1)}$. We remove the subpolynomial loss and prove that $K(S)\\geq c|S|^{1/5}$ for an absolute constant $c>0$. The proof combines two estimates from Bedert's argument with an exact averaging identity for the asymmetric boundaries of additive intersections. This identity replaces the multiplicative-amplification step responsible for the logarithmic loss.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05338",
  "author_total": 1,
  "authors": [
    {
      "name": "Abhishek Shankar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9k6zadjgaaah6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05338",
  "fulltext_url": null,
  "id": "9k6zadjgaaah6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05338",
  "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.CA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7211916610",
  "pdf_url": "https://arxiv.org/pdf/2609.05338",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9k6zadjgaaah6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05338",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05338"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Log-Free $n^{1/5}$ Bound for Chowla's Cosine Problem",
  "title_text": "A Log-Free n^1/5 Bound for Chowla's Cosine Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/9k6zadjgaaah6",
  "venue": "arXiv",
  "versions": []
}