{
  "id": "1904.02248",
  "version": "v1",
  "published": "2019-04-03T21:48:06.000Z",
  "updated": "2019-04-03T21:48:06.000Z",
  "title": "A $t$-motivic interpretation of shuffle relations for multizeta values",
  "authors": [
    "Wei-Cheng Huang"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Thakur (2010) showed that, for $r,$ $s\\in \\mathbb{N}$, a product of two Carlitz zeta values $\\zeta_A(r)$ and $\\zeta_A(s)$ can be expressed as an $\\mathbb{F}_p$-linear combination of $\\zeta_A(r+s)$ and double zeta values of weight $r+s$. Such an expression is called shuffle relation by Thakur. Fixing $r,$ $s\\in \\mathbb{N}$, we construct a $t$-module $E'$. To determine whether an $(r+s)$-tuple $\\mathfrak{C}$ in $\\mathbb{F}_q(\\theta)^{r+s}$ gives a shuffle relation, we relate it to the $\\mathbb{F}_q[t]$-torsion property of the point $\\mathbf{v}_\\mathfrak{C}\\in E'(\\mathbb{F}_q[\\theta])$ constructed with respect to the given $(r+s)$-tuple $\\mathfrak{C}$. We also provide an effective criterion for deciding the $\\mathbb{F}_q[t]$-torsion property of the point $\\mathbf{v}_\\mathfrak{C}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-03T21:48:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shuffle relation",
      "multizeta values",
      "motivic interpretation",
      "torsion property",
      "carlitz zeta values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}