{
  "id": "2209.01644",
  "version": "v1",
  "published": "2022-09-04T15:35:22.000Z",
  "updated": "2022-09-04T15:35:22.000Z",
  "title": "An introduction to decoupling and harmonic analysis over $\\mathbb{Q}_p$",
  "authors": [
    "Zane Kun Li"
  ],
  "comment": "26 pages",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "The goal of this expository paper is to provide an introduction to decoupling by working in the simpler setting of decoupling for the parabola over $\\mathbb{Q}_p$. Over $\\mathbb{Q}_p$, commonly used heuristics in decoupling are significantly easier to make rigorous over $\\mathbb{Q}_p$ than over $\\mathbb{R}$ and such decoupling theorems over $\\mathbb{Q}_p$ are still strong enough to derive interesting number theoretic conclusions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-04T15:35:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic analysis",
      "decoupling",
      "introduction",
      "derive interesting number theoretic conclusions",
      "expository paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}