{
  "id": "2401.01819",
  "version": "v1",
  "published": "2024-01-03T16:23:53.000Z",
  "updated": "2024-01-03T16:23:53.000Z",
  "title": "Arithmetic progression in a finite field with prescribed norms",
  "authors": [
    "Kaustav Chatterjee",
    "Hariom Sharma",
    "Aastha Shukla",
    "Shailesh Kumar Tiwari"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Given a prime power $q$ and a positive integer $n$, let $\\mathbb{F}_{q^{n}}$ represents a finite extension of degree $n$ of the finite field ${\\mathbb{F}_{q}}$. In this article, we investigate the existence of $m$ elements in arithmetic progression, where every element is primitive and at least one is normal with prescribed norms. Moreover, for $n\\geq6,q=3^k,m=2$ we establish that there are only $10$ possible exceptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-03T16:23:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12E20",
      "11T23"
    ],
    "keywords": [
      "finite field",
      "arithmetic progression",
      "prescribed norms",
      "prime power",
      "finite extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}