{
  "id": "1102.2295",
  "version": "v1",
  "published": "2011-02-11T07:32:27.000Z",
  "updated": "2011-02-11T07:32:27.000Z",
  "title": "On multiplicativity of Fourier coefficients at cusps other than infinity",
  "authors": [
    "Joseph Hundley"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper treats the problem of determining conditions for the Fourier coefficients of a Maass-Hecke newform at cusps other than infinity to be multiplicative. To be precise, the Fourier coefficients are defined using a choice of matrix in SL(2, Z) which maps infinity to the cusp in question. Let c and d be the entries in the bottom row of this matrix, and let N be the level. In earlier work with Dorian Goldfeld and Min Lee, we proved that the coefficients will be multiplicative whenever N divides 2cd. This paper proves that they will not be multiplicative unless N divides 576cd. Further, if one assumes that the Hecke eigenvalue vanishes less than half the time then this number drops to 48cd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-11T07:32:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30"
    ],
    "keywords": [
      "fourier coefficients",
      "multiplicativity",
      "hecke eigenvalue vanishes",
      "min lee",
      "maps infinity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.2295H"
    }
  }
}