{
  "as_of": "2026-09-05",
  "references": [
    {
      "title": "254A Notes 3: The large sieve and the Bombieri-Vinogradov theorem",
      "author": "Terence Tao",
      "date": "2015-01-10",
      "url": "https://terrytao.wordpress.com/2015/01/10/254a-notes-3-the-large-sieve-and-the-bombieri-vinogradov-theorem/",
      "used_for": "Pinned Vaughan identity, Lemma 18 equation (32)"
    },
    {
      "title": "On the distribution of alpha p modulo 1",
      "author": "R. C. Vaughan",
      "venue": "Mathematika 24 (1977), 135-141",
      "doi": "10.1112/S0025579300009025",
      "used_for": "Historical Vaughan method context"
    }
  ]
}