{
  "id": "2106.05213",
  "version": "v1",
  "published": "2021-06-09T16:57:05.000Z",
  "updated": "2021-06-09T16:57:05.000Z",
  "title": "Hilbert's Irreducibility, Modular Forms, and Computation of Certain Galois Groups",
  "authors": [
    "Iva Kodrnja",
    "Goran Muić"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we discuss applications of the theory developed in [21] and [22] in studying certain Galois groups and splitting fields of rational functions in $\\mathbb Q\\left(X_0(N)\\right)$ using Hilbert's irreducibility theorem and modular forms. We also consider computational aspect of the problem using MAGMA and SAGE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-09T16:57:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois groups",
      "modular forms",
      "hilberts irreducibility theorem",
      "rational functions",
      "computational aspect"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}