{
  "id": "1912.12084",
  "version": "v1",
  "published": "2019-12-27T13:17:10.000Z",
  "updated": "2019-12-27T13:17:10.000Z",
  "title": "CM values of higher automorphic Green functions for orthogonal groups",
  "authors": [
    "Jan Hendrik Bruinier",
    "Stephan Ehlen",
    "Tonghai Yang"
  ],
  "comment": "68 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function $G_s(z_1,z_2)$ for the elliptic modular group at positive integral spectral parameter $s$ are given by logarithms of algebraic numbers in suitable class fields. We prove a partial average version of this conjecture, where we sum in the first variable $z_1$ over all CM points of a fixed discriminant $d_1$ (twisted by a genus character), and allow in the second variable the evaluation at individual CM points of discriminant $d_2$. This result is deduced from more general statements for automorphic Green functions on Shimura varieties associated with the group $\\mathrm{GSpin}(n,2)$. We also use our approach to prove a Gross-Kohnen-Zagier theorem for higher Heegner divisors on Kuga-Sato varieties over modular curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-27T13:17:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "11G15",
      "11F37"
    ],
    "keywords": [
      "higher automorphic green functions",
      "cm values",
      "orthogonal groups",
      "positive integral spectral parameter",
      "individual cm points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 68,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}