{
  "id": "2305.06995",
  "version": "v1",
  "published": "2023-05-11T17:32:26.000Z",
  "updated": "2023-05-11T17:32:26.000Z",
  "title": "Bounds for theta sums in higher rank II",
  "authors": [
    "Jens Marklof",
    "Matthew Welsh"
  ],
  "comment": "26 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further improved for almost all parameter values. Our results extend the bound for one-variable theta sums obtained by Fedotov and Klopp in 2012.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-11T17:32:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "11L15",
      "37A17"
    ],
    "keywords": [
      "higher rank",
      "multi-variable exponential sums",
      "one-variable theta sums",
      "quadratic form",
      "first paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}