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
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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).