{
  "id": "2401.13725",
  "version": "v1",
  "published": "2024-01-24T18:10:03.000Z",
  "updated": "2024-01-24T18:10:03.000Z",
  "title": "Correlations of the squares of the Riemann zeta on the critical line",
  "authors": [
    "Valeriya Kovaleva"
  ],
  "comment": "58 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We compute the average of a product of two shifted squares of the Riemann zeta on the critical line with shifts up to size $T^{3/2-\\varepsilon}$. We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's. As a consequence, we also compute the $(2,2)$-moment of moment of the Riemann zeta, for which we partially verify (and partially refute) a conjecture of Bailey and Keating.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-24T18:10:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta",
      "critical line",
      "correlations",
      "error term similar",
      "approximate spectral expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}