{
  "id": "1903.06145",
  "version": "v1",
  "published": "2019-03-14T17:45:04.000Z",
  "updated": "2019-03-14T17:45:04.000Z",
  "title": "On the linear twist of degree 1 functions in the extended Selberg class",
  "authors": [
    "Giamila Zaghloul"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given a degree 1 function $F\\in\\mathcal{S}^{\\sharp}$ and a real number $\\alpha$, we consider the linear twist $F(s,\\alpha)$, proving that it satisfies a functional equation reflecting $s$ into $1-s$, which can be seen as a Hurwitz-Lerch type of functional equation. We also derive some results on the distribution of the zeros of the linear twist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-14T17:45:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41"
    ],
    "keywords": [
      "linear twist",
      "extended selberg class",
      "real number",
      "hurwitz-lerch type",
      "functional equation reflecting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}