{
  "id": "1603.01306",
  "version": "v1",
  "published": "2016-03-03T22:39:11.000Z",
  "updated": "2016-03-03T22:39:11.000Z",
  "title": "Zeros of certain combinations of Eisenstein series",
  "authors": [
    "Sarah Reitzes",
    "Polina Vulakh",
    "Matthew P. Young"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that if $k$ and $\\ell$ are sufficiently large, then all the zeros of the weight $k+\\ell$ cusp form $E_k(z) E_{\\ell}(z) - E_{k+\\ell}(z)$ in the standard fundamental domain lie on the boundary. We moreover find formulas for the number of zeros on the bottom arc with $|z|=1$, and those on the sides with $x = \\pm 1/2$. One important ingredient of the proof is an approximation of the Eisenstein series in terms of the Jacobi theta function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-03T22:39:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11"
    ],
    "keywords": [
      "eisenstein series",
      "combinations",
      "standard fundamental domain lie",
      "jacobi theta function",
      "cusp form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160301306R"
    }
  }
}