{
  "id": "1211.4715",
  "version": "v2",
  "published": "2012-11-20T11:27:40.000Z",
  "updated": "2013-03-22T14:07:16.000Z",
  "title": "Petersson inner products of weight one modular forms",
  "authors": [
    "Maryna Viazovska"
  ],
  "comment": "36 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we study regularized Petersson products between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight 1 modular form with integral Fourier coefficients. In our recent work \\cite{Via CM Green} motivated by the conjecture of B. Gross and D. Zagier on the CM values of higher Green's functions we have discovered that such a Petersson product is equal to the logarithm of a certain algebraic number lying in a ring class field associated to the binary quadratic form. The main result of the present paper is the explicit factorization formula for the obtained algebraic number.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-22T14:07:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "petersson inner products",
      "modular form",
      "algebraic number",
      "positive definite binary quadratic form",
      "explicit factorization formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4715V"
    }
  }
}