{
  "id": "2305.11492",
  "version": "v1",
  "published": "2023-05-19T07:45:34.000Z",
  "updated": "2023-05-19T07:45:34.000Z",
  "title": "Results on the Non-Vanishing of Derivatives of L-Functions of Vector-Valued Modular Forms",
  "authors": [
    "Subong Lim",
    "Wissam Raji"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2302.12576",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show a non-vanishing result for the averages of the derivatives of $L$-functions associated with the orthogonal basis of the space of vector-valued cusp forms of weight $k\\in \\frac12 \\mathbb{Z}$ on the full group in the critical strip. We also show the existence of at least one basis element whose $L$-function does not vanish under certain conditions. As an application, we generalize our result to Kohnen's plus space and prove an analogous result for Jacobi forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-19T07:45:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector-valued modular forms",
      "derivatives",
      "l-functions",
      "non-vanishing",
      "kohnens plus space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}