{
  "id": "1504.01307",
  "version": "v1",
  "published": "2015-04-06T15:40:17.000Z",
  "updated": "2015-04-06T15:40:17.000Z",
  "title": "The hyperbolic lattice point problem in conjugacy classes",
  "authors": [
    "Dimitrios Chatzakos",
    "Yiannis Petridis"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For $\\Gamma$ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice point problem. We use large sieve inequalities for the Riemann surfaces $\\Gamma\\backslash \\mathbb H$ to obtain average results for the error term, which are conjecturally optimal. We give a new proof of the error bound $O(X^{2/3})$, due to A. Good. For $\\hbox{SL}(2,{\\mathbb Z})$ we interpret our results in terms of indefinite quadratic forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-06T15:40:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F72",
      "37C35",
      "37D40"
    ],
    "keywords": [
      "conjugacy classes",
      "classical hyperbolic lattice point problem",
      "large sieve inequalities",
      "indefinite quadratic forms",
      "cofinite fuchsian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150401307C"
    }
  }
}