{
  "id": "1502.04603",
  "version": "v1",
  "published": "2014-11-25T16:53:18.000Z",
  "updated": "2014-11-25T16:53:18.000Z",
  "title": "Theta vocabulary I",
  "authors": [
    "S. Kharchev",
    "A. Zabrodin"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "This paper is an annotated list of transformation properties and identities satisfied by the four theta functions $\\theta _1$, $\\theta _2$, $\\theta _3$ $\\theta _4$ of one complex variable, presented in a ready-to-use form. An attempt is made to reveal a pattern behind various identities for the theta-functions. It is shown that all possible 3, 4 and 5-term identities of degree four emerge as algebraic consequences of the six fundamental bilinear 3-term identities connecting the theta-functions with modular parameters $\\tau$ and $2\\tau$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-25T16:53:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "theta vocabulary",
      "identities",
      "theta functions",
      "transformation properties",
      "modular parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150204603K"
    }
  }
}