{
  "id": "2205.08749",
  "version": "v1",
  "published": "2022-05-18T06:42:04.000Z",
  "updated": "2022-05-18T06:42:04.000Z",
  "title": "Convolution and square in abelian groups I",
  "authors": [
    "Yves Benoist"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that on the cyclic groups of odd order d, there exist non zero functions whose convolution square f*f(2t) is proportional to their square f(t)^2 when the proportionality constant is given by an imaginary quadratic integer of norm d which is equal to 1 modulo 2. The proof involves theta functions on elliptic curves with complex multiplication.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-18T06:42:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian groups",
      "non zero functions",
      "imaginary quadratic integer",
      "elliptic curves",
      "odd order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}