{
  "id": "2007.14008",
  "version": "v1",
  "published": "2020-07-28T06:24:28.000Z",
  "updated": "2020-07-28T06:24:28.000Z",
  "title": "Dirichlet Series with Periodic Coefficients and their Value-Distribution Near the Critical Line",
  "authors": [
    "Athanasios Sourmelidis",
    "Jörn Steuding",
    "Ade Irma Suriajaya"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters. We study the value-distribution of these Dirichlet series $L(s;f)$, resp. their analytic continuation in the neighborhood of the critical line (which is the abscissa of symmetry of the related Riemann-type functional equation). In particular, for a fixed complex number $a\\neq 0$, we prove for an even or odd periodic $f$ the number of $a$-points of the $\\Delta$-factor of the functional equation, prove the existence of the mean-value of the values of $L(s;f)$ taken at these points, show that the ordinates of these $a$-points are uniformly distributed modulo one and apply this to show a discrete universality theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-28T06:24:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "30D35"
    ],
    "keywords": [
      "dirichlet series",
      "critical line",
      "periodic coefficients",
      "value-distribution",
      "residue class characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}