{
  "id": "1210.7380",
  "version": "v1",
  "published": "2012-10-27T22:47:53.000Z",
  "updated": "2012-10-27T22:47:53.000Z",
  "title": "Estimates for the norms of products of sines and cosines",
  "authors": [
    "Jordan Bell"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "In this paper we prove asymptotic formulas for the $L^p$ norms of $P_n(\\theta)=\\prod_{k=1}^n (1-e^{ik\\theta})$ and $Q_n(\\theta)=\\prod_{k=1}^n (1+e^{ik\\theta})$. These products can be expressed using $\\prod_{k=1}^n \\sin\\Big(\\frac{k\\theta}{2}\\Big)$ and $\\prod_{k=1}^n \\cos\\Big(\\frac{k\\theta}{2}\\Big)$ respectively. We prove an estimate for $P_n$ at a point near where its maximum occurs. Finally, we give an asymptotic formula for the maximum of the Fourier coefficients of $Q_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-27T22:47:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A05",
      "26D05",
      "40A25"
    ],
    "keywords": [
      "asymptotic formula",
      "fourier coefficients",
      "maximum occurs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7380B"
    }
  }
}