{
  "id": "1910.09101",
  "version": "v1",
  "published": "2019-10-21T01:23:53.000Z",
  "updated": "2019-10-21T01:23:53.000Z",
  "title": "On a class of elliptic functions associated with the even Dirichlet characters",
  "authors": [
    "Dandan Chen",
    "Rong Chen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We construct a class of companion elliptic functions associated with the even Dirichlet characters. Using the well-known properties of the classical Weierstrass elliptic function $\\wp(z|\\tau)$ as the blueprint, we will derive their representations in terms of $q$-series and partial fractions, explore the significance of the coefficients of their power series expansions and establish the modular properties under the actions of the arithmetic groups $\\Gamma_0(N)$ and $\\Gamma_1(N)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-21T01:23:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet characters",
      "power series expansions",
      "companion elliptic functions",
      "classical weierstrass elliptic function",
      "partial fractions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}