{
  "id": "2008.13163",
  "version": "v1",
  "published": "2020-08-30T13:18:45.000Z",
  "updated": "2020-08-30T13:18:45.000Z",
  "title": "Explicit Relations between Kaneko--Yamamoto Type Multiple Zeta Values and Related Variants",
  "authors": [
    "Ce Xu",
    "Jianqiang Zhao"
  ],
  "comment": "32 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we first establish several integral identities. These integrals are of the form \\[\\int_0^1 x^{an+b} f(x)\\,dx\\quad (a\\in\\{1,2\\},\\ b\\in\\{-1,-2\\})\\] where $f(x)$ is a single-variable multiple polylogarithm function or $r$-variable multiple polylogarithm function or Kaneko--Tsumura A-function (this is a single-variable multiple polylogarithm function of level two). We find that these integrals can be expressed in terms of multiple zeta (star) values and their related variants (multiple $t$-values, multiple $T$-values, multiple $S$-values etc.), and multiple harmonic (star) sums and their related variants (multiple $T$-harmonic sums, multiple $S$-harmonic sums etc.). Using these integral identities, we prove many explicit evaluations of Kaneko--Yamamoto multiple zeta values and their related variants. Further, we derive some relations involving multiple zeta (star) values and their related variants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-30T13:18:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M32",
      "11M99",
      "11G55"
    ],
    "keywords": [
      "kaneko-yamamoto type multiple zeta values",
      "related variants",
      "explicit relations",
      "single-variable multiple polylogarithm function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}