JournalsrmiVol. 36, No. 7pp. 1957–1978

On the factorization of iterated polynomials

  • Lucas Reis

    Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
On the factorization of iterated polynomials cover
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Abstract

Let Fq\mathbb{F}_q be the finite field with qq elements and f,gFq[x]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))f(g^{(n)}(x)) over Fq\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).

Cite this article

Lucas Reis, On the factorization of iterated polynomials. Rev. Mat. Iberoam. 36 (2020), no. 7, pp. 1957–1978

DOI 10.4171/RMI/1187