{
  "id": "1212.5704",
  "version": "v2",
  "published": "2012-12-22T16:42:40.000Z",
  "updated": "2012-12-29T10:49:40.000Z",
  "title": "Explicit relations between primes in short intervals and exponential sums over primes",
  "authors": [
    "Alessandro Languasco",
    "Alessandro Zaccagnini"
  ],
  "comment": "one reference corrected",
  "categories": [
    "math.NT"
  ],
  "abstract": "Under the assumption of the Riemann Hypothesis (RH), we prove explicit quantitative relations between hypothetical error terms in the asymptotic formulae for truncated mean-square average of exponential sums over primes and in the mean-square of primes in short intervals. We also remark that such relations are connected with a more precise form of Montgomery's pair-correlation conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-29T10:49:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "11N05",
      "11M45"
    ],
    "keywords": [
      "short intervals",
      "exponential sums",
      "explicit relations",
      "montgomerys pair-correlation conjecture",
      "riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5704L"
    }
  }
}