Stable polynomials over finite fields

Domingo Gomez Perez, Alejandro P. Nicolas, Alina Ostafe, Daniel Sadornil

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We use the theory of resultants to study the stability, that is, the property of having all iterates irreducible, of an arbitrary polynomial f over a finite field F-q. This result partially generalizes the quadratic polynomial case described by R. Jones and N. Boston. Moreover, for p = 3, we show that certain polynomials of degree three are not stable. We also use the Weil bound for multiplicative character sums to estimate the number of stable polynomials over a finite field of odd characteristic.

Original languageEnglish
Pages (from-to)523-535
Number of pages13
JournalRevista Matematica Iberoamericana
Issue number2
Publication statusPublished - 2014
Externally publishedYes


  • Finite fields
  • irreducible polynomial
  • iterations of polynomials
  • discriminant
  • Discriminant
  • Irreducible polynomial
  • Iterations of polynomials


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