{
  "id": "2003.04350",
  "version": "v1",
  "published": "2020-03-09T18:32:45.000Z",
  "updated": "2020-03-09T18:32:45.000Z",
  "title": "The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces",
  "authors": [
    "Julia Brandes",
    "Scott T. Parsell"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We establish the analytic Hasse principle for Diophantine systems consisting of one diagonal form of degree $k$ and one general form of degree $d$, where $d$ is smaller than $k$. By employing a hybrid method that combines ideas from the study of general forms with techniques adapted to the diagonal case, we are able to obtain bounds that grow exponentially in $d$ but only quadratically in $k$, reflecting the growth rates typically obtained for both problems separately. We also discuss some of the most interesting generalisations of our approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-09T18:32:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D72",
      "11D45",
      "11P55",
      "14G05"
    ],
    "keywords": [
      "diagonal form",
      "lower-degree hypersurfaces",
      "general form",
      "analytic hasse principle",
      "hybrid method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}