{
  "id": "2401.09935",
  "version": "v2",
  "published": "2024-01-18T12:31:26.000Z",
  "updated": "2025-01-23T03:08:23.000Z",
  "title": "On finite analogues of Euler's constant",
  "authors": [
    "Masanobu Kaneko",
    "Toshiki Matsusaka",
    "Shin-ichiro Seki"
  ],
  "comment": "14 pages",
  "journal": "International Mathematics Research Notices, Volume 2025, Issue 2, January 2025, rnae281",
  "doi": "10.1093/imrn/rnae281",
  "categories": [
    "math.NT"
  ],
  "abstract": "We introduce and study finite analogues of Euler's constant in the same setting as finite multiple zeta values. We define a couple of candidate values from the perspectives of a ``regularized value of $\\zeta(1)$'' and of Mascheroni's and Kluyver's series expressions of Euler's constant using Gregory coefficients. Moreover, we reveal that the differences between them always lie in the $\\mathbb{Q}$-vector space spanned by 1 and values of a finite analogue of logarithm at positive integers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-23T03:08:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M32",
      "11B68",
      "11A07"
    ],
    "keywords": [
      "eulers constant",
      "finite multiple zeta values",
      "kluyvers series expressions",
      "study finite analogues",
      "vector space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}