{
  "id": "2410.16940",
  "version": "v1",
  "published": "2024-10-22T12:15:09.000Z",
  "updated": "2024-10-22T12:15:09.000Z",
  "title": "A segment of Euler product associated to a certain Dirichlet series",
  "authors": [
    "Rajat Gupta",
    "Aditi Savalia"
  ],
  "journal": "Journal of Number Theory, Volume 265, December 2024, Pages 270-290",
  "doi": "10.1016/j.jnt.2024.06.003",
  "categories": [
    "math.NT"
  ],
  "abstract": "In the spirit of the work of Hardy-Littlewood and Lavrik, we study the Dirichlet series associated to the generalized divisor function $\\sigma_{\\alpha}(n):=\\sum_{d|n}d^{\\alpha}$. We obtain an exact identity relating the Dirichlet series $\\zeta(s)\\zeta(s-\\alpha)$ and a segment of the Euler product attached to it. Specifically, our main theorems are valid in the critical strip.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-22T12:15:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "11M06"
    ],
    "keywords": [
      "dirichlet series",
      "euler product",
      "main theorems",
      "generalized divisor function",
      "exact identity relating"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}