{
  "id": "1602.01036",
  "version": "v1",
  "published": "2016-02-02T18:33:54.000Z",
  "updated": "2016-02-02T18:33:54.000Z",
  "title": "A note on cusp forms as $p$-adic limits",
  "authors": [
    "Scott Ahlgren",
    "Detchat Samart"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Several authors have recently proved results which express cusp forms as $p$-adic limits of weakly holomorphic modular forms under repeated application of Atkin's $U$-operator. The proofs involve techniques from the theory of weak harmonic Maass forms, and in particular a result of Guerzhoy, Kent, and Ono on the $p$-adic coupling of mock modular forms and their shadows. Here we obtain strengthened versions of these results using techniques from the theory of holomorphic modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-02T18:33:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33",
      "11F11",
      "11F03"
    ],
    "keywords": [
      "adic limits",
      "weak harmonic maass forms",
      "express cusp forms",
      "weakly holomorphic modular forms",
      "mock modular forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160201036A"
    }
  }
}