{
  "id": "1907.00188",
  "version": "v1",
  "published": "2019-06-29T12:00:12.000Z",
  "updated": "2019-06-29T12:00:12.000Z",
  "title": "Theta Blocks",
  "authors": [
    "Valery Gritsenko",
    "Nils-Peter Skoruppa",
    "Don Zagier"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We define theta blocks as products of Jacobi theta functions divided by powers of the Dedekind eta-function and show that they give a powerful new method to construct Jacobi forms and Siegel modular forms, with applications also in lattice theory and algebraic geometry. One of the central questions is when a theta block defines a Jacobi form. It turns out that this seemingly simple question is connected to various deep problems in different fields ranging from Fourier analysis over infinite-dimensional Lie algebras to the theory of moduli spaces in algebraic geometry. We give several answers to this question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-29T12:00:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F50"
    ],
    "keywords": [
      "algebraic geometry",
      "theta block defines",
      "jacobi theta functions",
      "define theta blocks",
      "construct jacobi forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}