{
  "id": "1405.7190",
  "version": "v2",
  "published": "2014-05-28T10:44:33.000Z",
  "updated": "2014-08-06T09:38:06.000Z",
  "title": "Resonances and $Ω$-results for Exponential Sums Related to Maass Forms for $\\mathrm{SL}(n,\\mathbb Z)$",
  "authors": [
    "Anne-Maria Ernvall-Hytönen",
    "Jesse Jääsaari",
    "Esa V. Vesalainen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We obtain resonances for short exponential sums involving Fourier coefficients of Maass forms for $\\mathrm{SL}(n,\\mathbb Z)$. This involves deriving asymptotics for the integrals appearing in the $\\mathrm{GL}(n)$ Voronoi summation formula. As an application, we also prove an $\\Omega$-result for short sums of Fourier coefficients.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-06T09:38:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential sums",
      "maass forms",
      "resonances",
      "fourier coefficients",
      "voronoi summation formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.7190E"
    }
  }
}