{
  "id": "2109.05661",
  "version": "v1",
  "published": "2021-09-13T01:20:45.000Z",
  "updated": "2021-09-13T01:20:45.000Z",
  "title": "On the distribution of traces of Frobenius for families of elliptic curves and the Lang-Trotter conjecture on average",
  "authors": [
    "Nathan Fugleberg",
    "Nahid Walji"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We obtain distribution results for traces of Frobenius for various families of elliptic curves with respect to the Lang-Trotter conjecture, extremal primes, and the central limit theorem. This includes some generalisations and bounds related to the work of Sha-Shparlinski on the average Lang-Trotter conjecture for single-parametric families of elliptic curves and the work of various authors on the trace of Frobenius for primes in congruence classes. Some results are also obtained for modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-13T01:20:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G20",
      "11N45"
    ],
    "keywords": [
      "elliptic curves",
      "central limit theorem",
      "average lang-trotter conjecture",
      "distribution results",
      "extremal primes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}