{
  "id": "1710.09869",
  "version": "v1",
  "published": "2017-10-26T18:56:10.000Z",
  "updated": "2017-10-26T18:56:10.000Z",
  "title": "Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field",
  "authors": [
    "Ian Petrow"
  ],
  "categories": [
    "math.NT",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to a congruence subgroup. Such an estimate has applications to the analytic theory of elliptic curves over a finite field, going beyond the Riemann hypothesis over finite fields. As the main tool to prove our bound on traces of Hecke operators, we develop a Petersson formula for newforms for general nebentype characters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-26T18:56:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F25",
      "11G20",
      "11T71"
    ],
    "keywords": [
      "hecke operator",
      "finite field",
      "elliptic curves",
      "applications",
      "holomorphic cusp forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}