The difference between permutation polynomials over finite fields

Stephen D. Cohen, Gary L. Mullen, Peter Jau Shyong Shiue

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Recently S. D. Cohen resolved a conjecture of Chowla and Zassenhaus (1968) in the affirmative by showing that, if f(x) and g(x) are integral polynomials of degree n ≥ 2 and p is a prime exceeding (n2 - 3n + 4)2 for which f and g are both permutation polynomials of the finite field Fp, then their difference h = f - g cannot be such that h(x) = ex for some integer c not divisible by p. In this note we provide a significant generalization by proving that, if h is not a constant in Fp and t is the degree of h, then and, provided t and n are not relatively prime. In a sense this measures the isolation of permutation polynomials of the same degree over large finite prime fields.

Original languageEnglish (US)
Pages (from-to)2011-2015
Number of pages5
JournalProceedings of the American Mathematical Society
Volume123
Issue number7
DOIs
StatePublished - Jul 1995

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'The difference between permutation polynomials over finite fields'. Together they form a unique fingerprint.

Cite this