{
  "id": "1503.00955",
  "version": "v1",
  "published": "2015-03-03T14:41:03.000Z",
  "updated": "2015-03-03T14:41:03.000Z",
  "title": "A note on the zeros of zeta and $L$-functions",
  "authors": [
    "Emanuel Carneiro",
    "Vorrapan Chandee",
    "Micah B. Milinovich"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi S(t)$ denote the argument of the Riemann zeta-function at the point $s=\\tfrac12+it$. Assuming the Riemann hypothesis, we give a new and simple proof of the sharpest known bound for $S(t)$. We discuss a generalization of this bound for a large class of $L$-functions including those which arise from cuspidal automorphic representations of GL($m$) over a number field. We also prove a number of related results including bounding the order of vanishing of an $L$-function at the central point and bounding the height of the lowest zero of an $L$-function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-03T14:41:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26",
      "11M36",
      "11M41",
      "41A30"
    ],
    "keywords": [
      "cuspidal automorphic representations",
      "riemann zeta-function",
      "riemann hypothesis",
      "lowest zero",
      "central point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}