On the factorization of iterated polynomials
Lucas Reis · Revista Matemática Iberoamericana · 2020
Let \mathbb{F}_q be the finite field with q elements and f, g\in \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).