{
  "id": "2204.10604",
  "version": "v1",
  "published": "2022-04-22T09:47:12.000Z",
  "updated": "2022-04-22T09:47:12.000Z",
  "title": "Deformations of Theta Integrals and A Conjecture of Gross-Zagier",
  "authors": [
    "Jan H. Bruinier",
    "Yingkun Li",
    "Tonghai Yang"
  ],
  "comment": "60 pages, comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we complete the proof of Gross-Zagier's conjecture concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over a real quadratic field, which is constructed as the Doi-Naganuma theta lift of a deformed theta integral on hyperbolic space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-22T09:47:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F37",
      "11F41",
      "11G15"
    ],
    "keywords": [
      "deformations",
      "gross-zagiers conjecture concerning algebraicity",
      "higher green functions",
      "real quadratic field",
      "single cm point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}