{
  "id": "2005.02393",
  "version": "v1",
  "published": "2020-05-05T16:56:09.000Z",
  "updated": "2020-05-05T16:56:09.000Z",
  "title": "Primes in arithmetic progressions and semidefinite programming",
  "authors": [
    "Andrés Chirre",
    "Valdir José Pereira Júnior",
    "David de Laat"
  ],
  "comment": "10 pages, 4 ancillary files",
  "categories": [
    "math.NT",
    "cs.NA",
    "math.CA",
    "math.NA"
  ],
  "abstract": "Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that contain primes from a given arithmetic progression using the approach developed by Carneiro, Milinovich and Soundararajan [Comment. Math. Helv. 94, no. 3 (2019)]. For this we extend the Guinand-Weil explicit formula over all Dirichlet characters modulo $q \\geq 3$, and we reduce the associated extremal problems to convex optimization problems that can be solved numerically via semidefinite programming.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-05T16:56:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11N13",
      "90C22"
    ],
    "keywords": [
      "arithmetic progression",
      "semidefinite programming",
      "convex optimization problems",
      "dirichlet characters modulo",
      "guinand-weil explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}