{
  "id": "1610.06900",
  "version": "v1",
  "published": "2016-10-21T19:22:34.000Z",
  "updated": "2016-10-21T19:22:34.000Z",
  "title": "The variance of divisor sums in arithmetic progressions",
  "authors": [
    "Brad Rodgers",
    "Kannan Soundararajan"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the variance of sums of the $k$-fold divisor function $d_k(n)$ over sparse arithmetic progressions, with averaging over both residue classes and moduli. In a restricted range, we confirm an averaged version of a recent conjecture about the asymptotics of this variance. This result is closely related to moments of Dirichlet $L$-functions and our proof relies on the asymptotic large sieve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-21T19:22:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divisor sums",
      "fold divisor function",
      "sparse arithmetic progressions",
      "asymptotic large sieve",
      "residue classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}