{
  "id": "2009.10774",
  "version": "v1",
  "published": "2020-09-22T19:21:11.000Z",
  "updated": "2020-09-22T19:21:11.000Z",
  "title": "Alternating Multiple $T$-Values: Weighted Sums, Duality, and Dimension Conjecture",
  "authors": [
    "Ce Xu",
    "Jianqiang Zhao"
  ],
  "comment": "33 page",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we define some weighted sums of the alternating multiple $T$-values (AMTVs), and study several duality formulas for them by using the tools developed in our previous papers. Then we introduce the alternating version of the convoluted $T$-values and Kaneko-Tsumura $\\psi$-function, which are proved to be closely related to the AMTVs. At the end of the paper, we study the $\\Q$-vector space generated by the AMTVs of any fixed weight $w$ and provide some evidence for the conjecture that their dimensions $\\{d_w\\}_{w\\ge 1}$ form the tribonacci sequence 1, 2, 4, 7, 13, ....",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-22T19:21:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M32",
      "11M35",
      "11G55",
      "11B39"
    ],
    "keywords": [
      "weighted sums",
      "alternating multiple",
      "dimension conjecture",
      "duality formulas",
      "vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}