{
  "annotation_id": "2ad4f853-fb4a-4eae-bcbc-b71d3fdf0685",
  "date_created": "2026-03-02T18:01:27.934000Z",
  "date_modified": "2026-03-02T18:01:27.934000Z",
  "file_hash": "ae764b4b1acd8a6a1736d63aac8600ddbe04c2f0f71cca05f813acc8fad1affe",
  "private": false,
  "record": {
    "abstract": "There is a simple, multi-sheet Riemann surface associated with e_q(z)\u0027s\ninverse function ln_q(w) for 0\u003c q \u003c 1. A principal sheet for ln_q(w) can be\ndefined. However, the topology of the Riemann surface for ln_q(w) changes each\ntime \"q\" increases above the collision point of a pair of the turning points of\ne_q(x). There is also a power series representation for ln_q(1+w). An\ninfinite-product representation for e_q(z) is used to obtain the ordinary\nnatural logarithm ln{e_q(z)} and the values of sum rules for the zeros \"z_i\" of\ne_q(z). For |z|\u003c|z_1|, e_q(z)=exp{b(z)} where b(z) is a simple, explicit power\nseries in terms of values of these sum rules. The values of the sum rules for\nthe q-trigonometric functions, sin_q(z) and cos_q(z), are q-deformations of the\nusual Bernoulli numbers.",
    "arxiv_id": "q-alg/9608015",
    "authors": [
      "Charles A. Nelson",
      "Michael G. Gartley"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1088/0305-4470/29/24/031",
    "title": "On the Two q-Analogue Logarithmic Functions",
    "url": "https://arxiv.org/abs/q-alg/9608015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7e41244b-5e97-4846-8748-cd7869868039",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}