{
  "annotation_id": "4b735790-ba6d-4665-87ec-6847a23cb87c",
  "date_created": "2026-02-17T05:53:20.519000Z",
  "date_modified": "2026-02-17T05:53:20.519000Z",
  "file_hash": "3718f3edb731485e22fc6034555089f0225924c8f2a90a717513ca755993bacd",
  "private": false,
  "record": {
    "abstract": "In this paper we investigate analytic inequalities related to a conjecture of Henry involving the difference between the Riemann zeta function and the digamma function. By treating $\\zeta(s)-\\psi(1-s)$ as a unified analytic object, we establish its strict convexity and monotonicity on suitable intervals. Moreover, we obtain explicit boundary limits of the derivative, expressed in terms of $\\pi$, $\\log (2\\pi)$ and Stieltjes constants. These results lead to new inequalities for $\\zeta(s)-\\psi(1-s)$ and shed further light on the conjecture.",
    "arxiv_id": "2601.09276",
    "authors": [
      "Liwen Gao",
      "Xuejun Guo"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Inequalities for $\\zeta(s)-\\psi(1-s)$ related to a conjecture of Henry",
    "url": "https://arxiv.org/abs/2601.09276",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "983da6c6-50d9-4cc1-bba3-8b8f98be685b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}