{
  "id": "2305.02989",
  "version": "v1",
  "published": "2023-05-04T16:57:12.000Z",
  "updated": "2023-05-04T16:57:12.000Z",
  "title": "Strong $q$-analogues for values of the Dirichlet beta function",
  "authors": [
    "Ankush Goswami",
    "Timothy Huber"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "An infinite class of relations between modular forms is constructed that generalizes evaluations of the Dirichlet beta function at odd positive integers. The work is motivated by a base case appearing in Ramanujan's Notebooks and a parallel construction for the Riemann zeta function. The identities are shown to be strong $q$-analogues by virtue of their reduction to the classical beta evaluations as $q\\to 1^{-}$ and explicit evaluations at CM points for $|q|<1$. Inequalities of Deligne determine asymptotic formulas for the Fourier coefficients of the associated modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-04T16:57:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11"
    ],
    "keywords": [
      "dirichlet beta function",
      "deligne determine asymptotic formulas",
      "riemann zeta function",
      "generalizes evaluations",
      "infinite class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}