{
  "id": "2205.08183",
  "version": "v1",
  "published": "2022-05-17T09:10:57.000Z",
  "updated": "2022-05-17T09:10:57.000Z",
  "title": "Hurwitz Zeta Functions and Ramanujan's Identity for Odd Zeta Values",
  "authors": [
    "Parth Chavan"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Inspired by a famous formula of Ramanujan for odd zeta values, we prove an analogous formula involving the Hurwitz zeta function. We introduce a new integral kernel related to the Hurwitz zeta function, generalizing the integral kernel associated to Ramanujan's identity. We also derive several infinite families of identities analogous to Ramanujan's formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-17T09:10:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hurwitz zeta function",
      "odd zeta values",
      "ramanujans identity",
      "integral kernel",
      "ramanujans formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}