{
  "id": "1501.04269",
  "version": "v1",
  "published": "2015-01-18T06:45:57.000Z",
  "updated": "2015-01-18T06:45:57.000Z",
  "title": "On the Tong-type identity and the mean square of the error term for an extended Selberg class",
  "authors": [
    "Xiaodong Cao",
    "Yoshio Tanigawa",
    "Wenguang Zhai"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In 1956, Tong established an asymptotic formula for the mean square of the error term in the summatory function of the Piltz divisor function $d_3(n).$ The aim of this paper is to generalize Tong's method to a class of Dirichlet series that satisfy a functional equation. As an application, we can establish the asymptotic formulas for the mean square of the error terms for a class of functions in the well-known Selberg class. The Tong-type identity and formula established in this paper can be viewed as an analogue of the well-known Vorono\\\"i's formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-18T06:45:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean square",
      "error term",
      "extended selberg class",
      "tong-type identity",
      "asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}