{
  "id": "2007.10249",
  "version": "v1",
  "published": "2020-07-20T16:39:15.000Z",
  "updated": "2020-07-20T16:39:15.000Z",
  "title": "On superorthogonality",
  "authors": [
    "Lillian B. Pierce"
  ],
  "comment": "61 pages. With an appendix by Emmanuel Kowalski",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "In this survey, we explore how superorthogonality amongst functions in a sequence $f_1,f_2,f_3,\\ldots$ results in direct or converse inequalities for an associated square function. We distinguish between three main types of superorthogonality, which we demonstrate arise in a wide array of settings in harmonic analysis and number theory. This perspective gives clean proofs of central results, and unifies topics including Khintchine's inequality, Walsh-Paley series, discrete operators, decoupling, counting solutions to systems of Diophantine equations, multicorrelation of trace functions, and the Burgess bound for short character sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-20T16:39:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "superorthogonality",
      "short character sums",
      "associated square function",
      "main types",
      "demonstrate arise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}