JournalsrmiVol. 30, No. 2pp. 523–535

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
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Abstract

We use the theory of resultants to study the stability, that is, the property of having all iterates irreducible, of an arbitrary polynomial ff over a finite field Fq\mathbb{F}_q. This result partially generalizes the quadratic polynomial case described by R. Jones and N. Boston. Moreover, for p=3p=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.

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