Stable polynomials over finite fields

  • Domingo Gómez-Pérez

    Universidad de Cantabria, Santander, Spain
  • Alejandro P. Nicolás

    Universidad de Valladolid, Spain
  • Alina Ostafe

    University of New South Wales, Sydney, Australia
  • Daniel Sadornil

    Universidad de Cantabria, Santander, Spain


We use the theory of resultants to study the stability, that is, the property of having all iterates irreducible, of an arbitrary polynomial over a finite field . This result partially generalizes the quadratic polynomial case described by R. Jones and N. Boston. Moreover, for , 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.

Cite this article

Domingo Gómez-Pérez, Alejandro P. Nicolás, Alina Ostafe, Daniel Sadornil, Stable polynomials over finite fields. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 523–535

DOI 10.4171/RMI/791