{
  "id": "1407.7285",
  "version": "v1",
  "published": "2014-07-27T21:23:08.000Z",
  "updated": "2014-07-27T21:23:08.000Z",
  "title": "An explicit approach to the Ahlgren-Ono conjecture",
  "authors": [
    "Geoffrey D. Smith",
    "Lynnelle Ye"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p(n)$ be the partition function. Ahlgren and Ono conjectured that every arithmetic progression contains infinitely many integers $N$ for which $p(N)$ is not congruent to $0\\pmod{3}$. Radu proved this conjecture in 2010 using work of Deligne and Rapoport. In this note, we give a simpler proof of Ahlgren and Ono's conjecture in the special case where the modulus of the arithmetic progression is a power of $3$ by applying a method of Boylan and Ono and using work of Bella\\\"iche and Khare generalizing Serre's results on the local nilpotency of the Hecke algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-27T21:23:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "ahlgren-ono conjecture",
      "explicit approach",
      "khare generalizing serres results",
      "arithmetic progression contains",
      "hecke algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7285S"
    }
  }
}