{
  "id": "2404.06016",
  "version": "v1",
  "published": "2024-04-09T04:51:48.000Z",
  "updated": "2024-04-09T04:51:48.000Z",
  "title": "Twisted Kronecker series and periods of modular forms on $Γ_0(N)$",
  "authors": [
    "Clifford Blakestad",
    "YoungJu Choie"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We introduce an infinite family of Kronecker series twisted by characters. As an application, we give a closed formula for the sum of all Hecke eigenforms on ${\\Gamma}_0(N) $ multiplied by their twisted period polynomials in terms of the product of those twisted Kronecker series, when N is square free. This extends an identity of Zagier among period polynomials, Hecke eigenforms and a quotient of Jacobi theta series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-09T04:51:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F12",
      "11F25",
      "11F50",
      "11F67"
    ],
    "keywords": [
      "twisted kronecker series",
      "modular forms",
      "hecke eigenforms",
      "jacobi theta series",
      "square free"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}