{
  "id": "2101.04418",
  "version": "v1",
  "published": "2021-01-12T11:39:25.000Z",
  "updated": "2021-01-12T11:39:25.000Z",
  "title": "Correlations of sieve weights and distributions of zeros",
  "authors": [
    "Aled Walker"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this note we give two small results concerning the correlations of the Selberg sieve weights. We then use these estimates to derive a new (conditional) lower bound on the variance of the primes in short intervals, and also on the so-called `form factor' for the pair correlations of the zeros of the Riemann zeta function. Our bounds ultimately rely on the estimates of Bettin--Chandee for trilinear Kloosterman fractions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-12T11:39:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distributions",
      "selberg sieve weights",
      "riemann zeta function",
      "trilinear kloosterman fractions",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}