On the factorization of iterated polynomials

2018/10/17 by Reis, Lucas
#37P05 (primary) and 12E05 (secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.07715

Abstract

Let \mathbb F_q be the finite field with q elements, f, g∈ \mathbb F_q[x] be polynomials of degree at least one. This paper deals with the asymptotic growth of certain arithmetic functions associated to the factorization of the iterated polynomials f(g⁽ⁿ⁾(x)) over \mathbb F_q, such as the largest degree of an irreducible factor and the number of irreducible factors. In particular, we provide significant improvements on the results of D. Gómez-Pérez, A. Ostafe and I. Shparlinski (2014).

Related

• Factorization of composed polynomials and applications
• Iterating additive polynomials over finite fields
• A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields
• On the distribution of polynomials having a given number of irreducible factors over finite fields
• Polynomial factorization over henselian fields