{
  "id": "1109.6697",
  "version": "v2",
  "published": "2011-09-30T00:34:58.000Z",
  "updated": "2012-10-16T13:50:35.000Z",
  "title": "An asymptotic formula for representations of integers by indefinite hermitian forms",
  "authors": [
    "Emilio A. Lauret"
  ],
  "comment": "To appear in Proceedings of the American Mathematical Society",
  "journal": "Proc. Amer. Math. Soc. 142 (2014), 1--14",
  "doi": "10.1090/S0002-9939-2013-11726-0",
  "categories": [
    "math.NT"
  ],
  "abstract": "We fix a maximal order $\\mathcal O$ in $\\F=\\R,\\C$ or $\\mathbb{H}$, and an $\\F$-hermitian form $Q$ of signature $(n,1)$ with coefficients in $\\mathcal O$. Let $k\\in\\N$. By applying a lattice point theorem on the $\\F$-hyperbolic space, we give an asymptotic formula with an error term, as $t\\to+\\infty$, for the number $N_t(Q,-k)$ of integral solutions $x\\in\\mathcal O^{n+1}$ of the equation $Q[x]=-k$ satisfying $|x_{n+1}|\\leq t$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-16T13:50:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "11E39",
      "58C40"
    ],
    "keywords": [
      "indefinite hermitian forms",
      "asymptotic formula",
      "representations",
      "lattice point theorem",
      "maximal order"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6697L"
    }
  }
}