{
  "id": "1704.05834",
  "version": "v1",
  "published": "2017-04-19T17:43:02.000Z",
  "updated": "2017-04-19T17:43:02.000Z",
  "title": "On large gaps between zeros of $L$-functions from branches",
  "authors": [
    "André LeClair"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is commonly believed that the normalized gaps between consecutive ordinates $t_n$ of the zeros of the Riemann zeta function on the critical line can be arbitrarily large. In particular, drawing on analogies with random matrix theory, it has been conjectured that $$\\lambda' ={ lim ~ sup} ~( t_{n+1} - t_n ) \\frac{ \\log( t_n /2 \\pi e)}{2\\pi}$$ equals $\\infty$. In this article we provide arguments, although not a rigorous proof, that $\\lambda'$ is finite. A short argument, conditional on the Riemann Hypothesis, gives $\\lambda' \\geq 3$. Additional arguments lead us to propose $\\lambda'\\leq 5$. This proposal is consistent with numerous calculations that place lower bounds on $\\lambda'$. We present the generalization of this result to all Dirichlet $L$-functions and those based on cusp forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-19T17:43:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large gaps",
      "riemann zeta function",
      "random matrix theory",
      "place lower bounds",
      "riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}