On the factorization of iterated polynomials

Lucas Reis ^[1]
1. [1] Universidade Federal de Minas Gerais
  
  Universidade Federal de Minas Gerais
  
  Brasil
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 7, 2020, págs. 1957-1978
Idioma: inglés
DOI: 10.4171/rmi/1187
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Resumen
- Let Fq be the finite field with q elements and f,g∈Fq[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 Fq, 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).