{
  "id": "2106.12953",
  "version": "v1",
  "published": "2021-06-24T12:22:51.000Z",
  "updated": "2021-06-24T12:22:51.000Z",
  "title": "On the vanishing of some mock theta functions at odd roots of unity",
  "authors": [
    "Mohamed El Bachraoui"
  ],
  "comment": "Accepted in Research in Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider the problem of whether or not certain mock theta functions vanish at the roots of unity with an odd order. We prove for any such function $f(q)$ that there exists a constant $C>0$ such that for any odd integer $n>C$ the function $f(q)$ does vanish at the primitive $n$-th roots of unity. This leads us to conjecture that $f(q)$ does not vanish at the primitive $n$-th roots of unity for any odd positive integer $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-24T12:22:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "odd roots",
      "th roots",
      "odd integer",
      "odd order",
      "mock theta functions vanish"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}