{
  "id": "1503.03119",
  "version": "v1",
  "published": "2015-03-10T23:03:20.000Z",
  "updated": "2015-03-10T23:03:20.000Z",
  "title": "Distribution of the values of the derivative of the Dirichlet $L$-functions at its $a$-points",
  "authors": [
    "Mohamed Taïb Jakhlouti",
    "Kamel Mazhouda"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study the value distribution of the Dirichlet $L$-function derivative $L'(s,\\chi)$ at the $a$-points $\\rho_{a,\\chi}=\\beta_{a,\\chi}+i\\gamma_{a,\\chi}$ of $L(s,\\chi).$ Actually, we give an asymptotic formula for the sum $$\\sum_{\\rho_{a,\\chi};\\ 0<\\gamma_{a,\\chi}\\leq T}L'(\\rho_{a,\\chi},\\chi) X^{\\rho_{a,\\chi}}\\ \\ \\hbox{as}\\ \\ T\\longrightarrow \\infty,$$ where $X$ is a fixed positive number and $\\chi$ is a primitive character $\\mod q$. This work continues the investigations of Fujii \\cite{2,3,4}, Garunk$\\check{s}$tis & Steuding \\cite{7} and the authors \\cite{12}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-10T23:03:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derivative",
      "value distribution",
      "asymptotic formula",
      "work continues",
      "positive number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}