{
  "id": "0707.1496",
  "version": "v1",
  "published": "2007-07-10T17:02:47.000Z",
  "updated": "2007-07-10T17:02:47.000Z",
  "title": "Subsets of F_p^n without three term arithmetic progressions have several large Fourier coefficients",
  "authors": [
    "Ernie Croot"
  ],
  "comment": "This is a preliminary draft. Later drafts will have more references and cleaner proofs",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Suppose that f : F_p^n -> [0,1] has expected value t in [p^(-n/9),1] (so, the density t can be quite low!). Furthermore, suppose that support(f) has no three-term arithmetic progressions. Then, we develop non-trivial lower bounds for f_j, which is the jth largest Fourier coefficient of f. This result is similar in spirit to that appearing in an earlier paper [1] by the author; however, in that paper the focus was on the ``small'' Fourier coefficients, whereas here the focus is on the ``large'' Fourier coefficients. Furthermore, the proof in the present paper requires much more sophisticated arguments than those of that other paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-10T17:02:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D99"
    ],
    "keywords": [
      "large fourier coefficients",
      "jth largest fourier coefficient",
      "non-trivial lower bounds",
      "three-term arithmetic progressions",
      "quite low"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.1496C"
    }
  }
}