{
  "id": "1505.02711",
  "version": "v1",
  "published": "2015-05-11T17:43:37.000Z",
  "updated": "2015-05-11T17:43:37.000Z",
  "title": "Singular moduli of higher level and special cycles",
  "authors": [
    "Stephan Ehlen"
  ],
  "comment": "25 pages; accepted for publication in Research in the Mathematical Sciences",
  "categories": [
    "math.NT"
  ],
  "abstract": "We describe the complex multiplication (CM) values of modular functions for $\\Gamma_0(N)$ whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply to Borcherds products of weight $0$ for $\\Gamma_0(N)$. By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-11T17:43:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11G15"
    ],
    "keywords": [
      "special cycles",
      "singular moduli",
      "higher level",
      "prime ideal factorizations",
      "cm elliptic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}