{
  "id": "math/9909190",
  "version": "v1",
  "published": "1999-09-08T00:00:00.000Z",
  "updated": "1999-09-08T00:00:00.000Z",
  "title": "The spectrum of multiplicative functions",
  "authors": [
    "Andrew Granville",
    "K. Soundararajan"
  ],
  "comment": "Abstract added in migration",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let S be a subset of the unit disk, and let F(s) denote the class of completely multiplicative functions f such that f(p) is in S for all primes p. The authors' main concern is which numbers arise as mean-values of functions in F(s). More precisely, let Gamma_N(S) = {1/N sum_{n <= N} f(n): f in F(S)} and Gamma(S) = lim_{N -> infinity} Gamma_N(s). The authors call Gamma(S) the spectrum of the set S, and study its properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-09-08T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicative functions",
      "numbers arise",
      "unit disk",
      "mean-values",
      "properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......9190G"
    }
  }
}