{
  "id": "1905.05260",
  "version": "v1",
  "published": "2019-05-13T19:37:13.000Z",
  "updated": "2019-05-13T19:37:13.000Z",
  "title": "Torsions in Cohomology of $\\text{SL}_2(\\mathbb{Z})$ and Congruence of Modular Forms",
  "authors": [
    "Taiwang Deng"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We describe torsion classes in the first cohomology group of $\\text{SL}_2(\\mathbb{Z})$. In particular, we obtain generalized Dickson's invariants for p-power polynomial rings. Secondly, we describe torsion classes in the zero-th homology group of $\\text{SL}_2(\\mathbb{Z})$ as a module over the torsion invariants. As application, we obtain various congruences between cuspidal forms of level one and Eisenstein series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-13T19:37:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular forms",
      "congruence",
      "torsion classes",
      "first cohomology group",
      "p-power polynomial rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}