{
  "id": "0904.2179",
  "version": "v2",
  "published": "2009-04-14T20:26:57.000Z",
  "updated": "2009-08-18T13:42:23.000Z",
  "title": "Kernels of $L$-functions of cusp forms",
  "authors": [
    "Nikolaos Diamantis",
    "Cormac O'Sullivan"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications, it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin's Periods Theorem. Cohen's representation of these kernels as series is also generalized.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-18T13:42:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F67"
    ],
    "keywords": [
      "cusp form",
      "manins periods theorem",
      "inner product",
      "cohens representation",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2179D"
    }
  }
}