{
  "id": "2505.02202",
  "version": "v1",
  "published": "2025-05-04T17:49:08.000Z",
  "updated": "2025-05-04T17:49:08.000Z",
  "title": "Multiple polylogarithms and the Steinberg module",
  "authors": [
    "Steven Charlton",
    "Danylo Radchenko",
    "Daniil Rudenko"
  ],
  "comment": "59 pages",
  "categories": [
    "math.NT",
    "math.AG",
    "math.AT",
    "math.KT"
  ],
  "abstract": "We establish a connection between multiple polylogarithms on a torus and the Steinberg module of $\\mathbb{Q}$, and show that multiple polylogarithms of depth $d$ and weight $n$ can be expressed via a single function $\\mathrm{Li}_{n-d+1,1,\\dots,1}(x_1,x_2,\\dots,x_d)$. Using this connection, we give a simple proof of the Bykovski\\u{\\i} theorem, explain the duality between multiple polylogarithms and iterated integrals, and provide a polylogarithmic interpretation of the conjectures of Rognes and Church-Farb-Putman.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-04T17:49:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G55",
      "19D45"
    ],
    "keywords": [
      "multiple polylogarithms",
      "steinberg module",
      "connection",
      "single function",
      "simple proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}