{
  "id": "1111.0241",
  "version": "v2",
  "published": "2011-11-01T16:49:26.000Z",
  "updated": "2011-11-11T01:28:27.000Z",
  "title": "Asymptotic expansion of the difference of two Mahler measures",
  "authors": [
    "John D. Condon"
  ],
  "comment": "25 pages. V2: Demoted previous Corollary 1 to a comment, after realizing that Boyd had already proved that bit. Made small corrections to Lemma 5, streamlined the proof of Lemma 9, and reworded section 9.3",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that for almost every polynomial P(x,y) with complex coefficients, the difference of the logarithmic Mahler measures of P(x,y) and P(x,x^n) can be expanded in a type of formal series similar to an asymptotic power series expansion in powers of 1/n. This generalizes a result of Boyd. We also show that such an expansion is unique and provide a formula for its coefficients. When P has algebraic coefficients, the coefficients in the expansion are linear combinations of polylogarithms of algebraic numbers, with algebraic coefficients.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-11T01:28:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C08",
      "11R06",
      "41A60"
    ],
    "keywords": [
      "asymptotic expansion",
      "difference",
      "asymptotic power series expansion",
      "algebraic coefficients",
      "logarithmic mahler measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.0241C"
    }
  }
}