{
  "id": "2112.10561",
  "version": "v2",
  "published": "2021-12-20T14:32:10.000Z",
  "updated": "2022-02-24T18:23:03.000Z",
  "title": "On the Epstein zeta function and the zeros of a class of Dirichlet series",
  "authors": [
    "Pedro Ribeiro",
    "Semyon Yakubovich"
  ],
  "comment": "typos corrected; added corollary 4.5 and example 5.6",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "By generalizing the classical Selberg-Chowla formula, we establish the analytic continuation and functional equation for a large class of Epstein zeta functions. This continuation is studied in order to provide new classes of theorems regarding the distribution of zeros of Dirichlet series in their critical lines and to produce a new method for the study of these problems. Due to the symmetries provided by the representation via the Selberg-Chowla formula, some generalizations of well-known formulas in analytic number theory are also deduced as examples.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-24T18:23:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "epstein zeta function",
      "dirichlet series",
      "analytic number theory",
      "classical selberg-chowla formula",
      "analytic continuation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}