{
  "id": "0803.2483",
  "version": "v1",
  "published": "2008-03-17T16:58:29.000Z",
  "updated": "2008-03-17T16:58:29.000Z",
  "title": "Value distribution of cyclotomic polynomial coefficients",
  "authors": [
    "Yves Gallot",
    "Pieter Moree",
    "Huib Hommersom"
  ],
  "comment": "26 pages, 6 tables. Partly based on arXiv:math.NT/0307352, which is the M.Sc. thesis of H. Hommersom (2003), enriched with research results due to Moree. Some of these research results have been extracted and various new results added. A connection with reciprocal cyclotomic polynomials (arXiv:0709.1570) is also made",
  "journal": "Unif. Distrib. Theory 6 (2011), 177-206",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let a_n(k) be the kth coefficient of the nth cyclotomic polynomial Phi_n(x). As n ranges over the integers, a_n(k) assumes only finitely many values. For any such value v we determine the density of integers n such that a_n(k)=v. Also we study the average of the a_n(k). We derive analogous results for the kth Taylor coefficient of 1/Phi_n(x) (taken around x=0), the kth coefficient of the nth reciprocal cyclotomic polynomial. We formulate various open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-17T16:58:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11B83"
    ],
    "keywords": [
      "cyclotomic polynomial coefficients",
      "value distribution",
      "kth coefficient",
      "nth reciprocal cyclotomic polynomial",
      "nth cyclotomic polynomial"
    ],
    "tags": [
      "dissertation",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.2483G"
    }
  }
}