{
  "id": "2206.09134",
  "version": "v1",
  "published": "2022-06-18T07:08:56.000Z",
  "updated": "2022-06-18T07:08:56.000Z",
  "title": "A modular relation involving non-trivial zeros of the Dedekind zeta function, and the Generalized Riemann Hypothesis",
  "authors": [
    "Atul Dixit",
    "Shivajee Gupta",
    "Akshaa Vatwani"
  ],
  "comment": "To appear in Journal of Mathematical Analysis and Applications",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a number field analogue of a result of Ramanujan, Hardy and Littlewood, thereby obtaining a modular relation involving the non-trivial zeros of the Dedekind zeta function. We also provide a Riesz-type criterion for the Generalized Riemann Hypothesis for $\\zeta_K(s)$. New elegant transformations are obtained when $K$ is a quadratic extension, one of which involves the modified Bessel function of the second kind.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-18T07:08:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dedekind zeta function",
      "generalized riemann hypothesis",
      "non-trivial zeros",
      "modular relation",
      "number field analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}