{
  "abstract": "Let lambda(n) denote the infimum of -min_x sum_{a in A} cos(ax) over all sets A of n positive integers. While the classical Sidon-difference construction yields lambda(n) <= (1 + o(1))sqrt(n)/2, we construct sets achieving a leading constant of 1/2: lambda(n) <= (1/2)sqrt(n) + O(n^(1/4)sqrt(log n)), establishing limsup_{n->infinity} lambda(n)/sqrt(n) <= 1/2. This construction combines a two-sided Sidon square identity, a Singer difference set, a Fejer-kernel majorant, a parity-biased deletion, and an exact-cardinality probabilistic selection. We also provide an L^4 criterion and a multiplicity bound constraining any construction with a smaller leading constant. In the opposite direction, we incorporate the L^1 norm into Bedert's boundary estimate with an explicit constant, yielding two lower bounds for f_A(x) = sum_{a in A} cos(ax): (1) -min f_A >= cn^(1/4) for every n-element set A subset of [1, Cn]; and (2) (-min f_A)^3 ||f_A||_1^2 >= cn for every n-element set A subset of N. The second bound recovers the 1/5 exponent of Bedert and Shankar and improves it whenever ||f_A||_1 is small relative to -min f_A. Numerical values of the construction are reported up to |A| = 25,440.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17160",
  "author_total": 6,
  "authors": [
    {
      "name": "Bryan Bu"
    },
    {
      "name": "Fayzan Khan"
    },
    {
      "name": "Hyunjun Yi"
    },
    {
      "name": "Atharv Jha"
    },
    {
      "name": "Ishaan Chandupatla"
    },
    {
      "name": "Madhav Nagpal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/69p9ge89d3f54.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17160",
  "fulltext_url": null,
  "id": "69p9ge89d3f54",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17160",
  "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": "W7221786781",
  "pdf_url": "https://arxiv.org/pdf/2610.17160",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/69p9ge89d3f54.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.17160",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17160"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Half-Constant Upper Bound for Chowla's Cosine Problem",
  "title_text": "A Half-Constant Upper Bound for Chowla's Cosine Problem",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/69p9ge89d3f54",
  "venue": "arXiv",
  "versions": []
}