{
  "id": "2208.09882",
  "version": "v1",
  "published": "2022-08-21T13:30:58.000Z",
  "updated": "2022-08-21T13:30:58.000Z",
  "title": "General coefficient-vanishing results associated with theta series",
  "authors": [
    "Shane Chern",
    "Dazhao Tang"
  ],
  "comment": "72 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In previous literature, there are a number of sporadic coefficient-vanishing results associated with theta series. These examples suggest certain underlying patterns. By expanding theta powers as a linear combination of products of theta functions, we present two strategies that will provide a unified treatment. Our approaches rely on studying the behavior of a product of two theta series under the action of the huffing operator. Some explicit criteria are given. We may use the presented method to not only verify experimentally discovered coefficient-vanishing results, but also to generate a series of general phenomena.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-21T13:30:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "11B65",
      "11J13",
      "11J20"
    ],
    "keywords": [
      "theta series",
      "general coefficient-vanishing results",
      "general phenomena",
      "explicit criteria",
      "sporadic coefficient-vanishing results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 72,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}