{
  "id": "2108.10238",
  "version": "v1",
  "published": "2021-08-23T15:21:58.000Z",
  "updated": "2021-08-23T15:21:58.000Z",
  "title": "On the $q$-analogue of the pair correlation conjecture via Fourier optimization",
  "authors": [
    "Oscar E. Quesada-Herrera"
  ],
  "comment": "17 pages, 3 figures",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "We study the $q$-analogue of the average of Montgomery's function $F(\\alpha, T)$ over bounded intervals. Assuming the Generalized Riemann Hypothesis for Dirichlet $L$-functions, we obtain upper and lower bounds for this average over an interval that are quite close to the pointwise conjectured value of 1. To compute our bounds, we extend a Fourier analysis approach by Carneiro, Chandee, Chirre, and Milinovich, and apply computational methods of non-smooth programming.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-23T15:21:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26",
      "41A30"
    ],
    "keywords": [
      "pair correlation conjecture",
      "fourier optimization",
      "fourier analysis approach",
      "generalized riemann hypothesis",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}