{
  "id": "2306.10218",
  "version": "v1",
  "published": "2023-06-17T00:46:05.000Z",
  "updated": "2023-06-17T00:46:05.000Z",
  "title": "Bounds for orders of zeros of a class of Eisenstein series and their applications on dual pairs of eta quotients",
  "authors": [
    "Amir Akbary",
    "Zafer Selcuk Aygin"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k$ be an even positive integer, $p$ be a prime and $m$ be a nonnegative integer. We find an upper bound for orders of zeros (at cusps) of a linear combination of classical Eisenstein series of weight $k$ and level $p^m$. As an immediate consequence we find the set of all eta quotients that are linear combinations of these Eisenstein series and hence the set of all eta quotients of level $p^m$ whose derivatives are also eta quotients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-17T00:46:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F20",
      "11F27"
    ],
    "keywords": [
      "eta quotients",
      "dual pairs",
      "applications",
      "linear combination",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}