{
  "id": "0902.2496",
  "version": "v1",
  "published": "2009-02-14T21:31:31.000Z",
  "updated": "2009-02-14T21:31:31.000Z",
  "title": "A non-split sum of coefficients of modular forms",
  "authors": [
    "Nicolas Templier"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We shall introduce and study certain truncated sums of Hecke eigenvalues of $GL_2$-automorphic forms along quadratic polynomials. A power saving estimate is established and new applications to moments of critical $L$-values associated to quadratic fields are derived. An application to the asymptotic behavior of the height of Heegner points and singular moduli is discussed in details.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-14T21:31:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L07",
      "11F30"
    ],
    "keywords": [
      "modular forms",
      "non-split sum",
      "coefficients",
      "singular moduli",
      "heegner points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2496T"
    }
  }
}