Stable polynomials over finite fields

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

doi:10.4171/RMI/791

Stable polynomials over finite fields

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

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	523-535
Number of pages	13
Journal	Revista Matematica Iberoamericana
Volume	30
Issue number	2
DOIs	https://doi.org/10.4171/RMI/791
Publication status	Published - 2014
Externally published	Yes

Keywords

Finite fields
irreducible polynomial
iterations of polynomials
discriminant
QUADRATIC POLYNOMIALS
PRIME
Discriminant
Irreducible polynomial
Iterations of polynomials

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10.4171/RMI/791

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T1 - Stable polynomials over finite fields

AU - Gomez Perez, Domingo

AU - Nicolas, Alejandro P.

AU - Ostafe, Alina

AU - Sadornil, Daniel

PY - 2014

Y1 - 2014

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AB - 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.

KW - Finite fields

KW - irreducible polynomial

KW - iterations of polynomials

KW - discriminant

KW - QUADRATIC POLYNOMIALS

KW - PRIME

KW - Discriminant

KW - Irreducible polynomial

KW - Iterations of polynomials

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VL - 30

SP - 523

EP - 535

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 2

ER -

Stable polynomials over finite fields

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Keywords

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