- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
30
2014
2
Stable polynomials over finite fields
Domingo
Gómez-Pérez
Universidad de Cantabria, SANTANDER, SPAIN
Alejandro
Nicolás
Universidad de Valladolid, VALLADOLID, SPAIN
Alina
Ostafe
University of New South Wales, SYDNEY, NSW, AUSTRALIA
Daniel
Sadornil
Universidad de Cantabria, SANTANDER, SPAIN
Finite fields, irreducible polynomial, iterations of polynomials, discriminant
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 $\mathbb{F}_q$. 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.
Number theory
523
535
10.4171/RMI/791
http://www.ems-ph.org/doi/10.4171/RMI/791