{
  "id": "1607.00469",
  "version": "v1",
  "published": "2016-07-02T05:16:05.000Z",
  "updated": "2016-07-02T05:16:05.000Z",
  "title": "On Eisenstein primes",
  "authors": [
    "Mayank Pandey"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we prove that there are infinitely many primes of the form $\\ell^2 - \\ell m + m^2$ such that $2\\ell - m$ is also prime. To prove this, we follow along the lines of the work of Fouvry and Iwaniec (1997) who showed that there are infinitely many primes of the form $\\ell^2 + m^2$ for $\\ell$ prime, but use $\\mathbb{Z}[\\omega]$ instead of $\\mathbb{Z}[i]$ to work with the bilinear forms that arise in both.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-02T05:16:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eisenstein primes",
      "bilinear forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}