{
  "id": "2211.03605",
  "version": "v1",
  "published": "2022-11-07T14:51:20.000Z",
  "updated": "2022-11-07T14:51:20.000Z",
  "title": "Polynomial equations for additive functions I",
  "authors": [
    "Eszter Gselmann",
    "Gergely Kiss"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the following type of equation is considered $$\\sum_{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x^{q_{i}})= 0 \\qquad \\left(x\\in \\mathbb{F}\\right),$$ where $n$ is a positive integer, $\\mathbb{F}\\subset \\mathbb{C}$ is a field, $f_{i}, g_{i}\\colon \\mathbb{F}\\to \\mathbb{C}$ are additive functions and $p_i, q_i$ are positive integers for all $i=1, \\ldots, n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-07T14:51:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16W20",
      "39B32",
      "43A45"
    ],
    "keywords": [
      "additive functions",
      "polynomial equations",
      "positive integer",
      "characterization theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}