{
  "id": "1701.02018",
  "version": "v1",
  "published": "2017-01-08T21:27:14.000Z",
  "updated": "2017-01-08T21:27:14.000Z",
  "title": "Averages of shifted convolution sums for $GL(3) \\times GL(2)$",
  "authors": [
    "Qingfeng Sun"
  ],
  "comment": "15 pages. Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A_f(1,n)$ be the normalized Fourier coefficients of a $GL(3)$ Maass cusp form $f$ and let $a_g(n)$ be the normalized Fourier coefficients of a $GL(2)$ cusp form $g$. Let $\\lambda(n)$ be either $A_f(1,n)$ or the triple divisor function $d_3(n)$. It is proved that for any $\\epsilon>0$, any integer $r\\geq 1$ and $r^{5/2}X^{1/4+7\\delta/2}\\leq H\\leq X$ with $\\delta>0$, $$ \\frac{1}{H}\\sum_{h\\geq 1}W\\left(\\frac{h}{H}\\right) \\sum_{n\\geq 1}\\lambda(n)a_g(rn+h)V\\left(\\frac{n}{X}\\right)\\ll X^{1-\\delta+\\epsilon}, $$ where $V$ and $W$ are smooth compactly supported functions, and the implied constants depend only on the associated forms and $\\epsilon$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-08T21:27:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shifted convolution sums",
      "normalized fourier coefficients",
      "maass cusp form",
      "triple divisor function",
      "smooth compactly supported functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}