{
  "id": "1602.00099",
  "version": "v1",
  "published": "2016-01-30T10:17:48.000Z",
  "updated": "2016-01-30T10:17:48.000Z",
  "title": "The Stokes phenomenon and the Lerch zeta function",
  "authors": [
    "R B Paris"
  ],
  "comment": "13 pages, 0 figures. arXiv admin note: text overlap with arXiv:1407.2782",
  "categories": [
    "math.CA"
  ],
  "abstract": "We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\\lambda,a,s)=\\sum_{n=1}^\\infty \\exp (2\\pi ni\\lambda)/(n+a)^s$ for large complex values of $a$, with $\\lambda$ and $s$ regarded as parameters. It is shown that an infinite number of subdominant exponential terms switch on across the Stokes lines $\\arg\\,a=\\pm\\pi/2$. In addition, it is found that the transition across the upper and lower imaginary $a$-axes is associated, in general, with unequal scales. Numerical calculations are presented to confirm the theoretical predictions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-30T10:17:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M35",
      "30E15",
      "34E05",
      "41A30",
      "41A60"
    ],
    "keywords": [
      "lerch zeta function",
      "stokes phenomenon",
      "subdominant exponential terms switch",
      "large complex values",
      "asymptotic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160200099P"
    }
  }
}