{
  "id": "2307.00256",
  "version": "v1",
  "published": "2023-07-01T07:35:31.000Z",
  "updated": "2023-07-01T07:35:31.000Z",
  "title": "Murmurations of Dirichlet characters",
  "authors": [
    "Kyu-Hwan Lee",
    "Thomas Oliver",
    "Alexey Pozdnyakov"
  ],
  "comment": "11 pages, 5 figures, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Inspired by recent observations for elliptic curves, we prove murmuration formulas connected to the local averages of Dirichlet characters, normalized by their Gauss sums, over geometric and short intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-01T07:35:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet characters",
      "elliptic curves",
      "murmuration formulas",
      "local averages"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}