On the factorization of iterated polynomials

Lucas Reis

On the factorization of iterated polynomials

Number Theory 2019-08-06 v2

Authors: Lucas Reis

Abstract

Let $\mathbb F_q$ be the finite field with $q$ elements, $f, g\in \mathbb F_q[x]$ 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. G\'{o}mez-P\'{e}rez, A. Ostafe and I. Shparlinski (2014).

Keywords

polynomials over finite fields finite fields polynomial theory

Cite

@article{arxiv.1810.07715,
  title  = {On the factorization of iterated polynomials},
  author = {Lucas Reis},
  journal= {arXiv preprint arXiv:1810.07715},
  year   = {2019}
}

Comments

The new version improves the readability of some proofs and corrects many minor issues. ***To appear in Rev. Mat. Iberoamericana

On the factorization of iterated polynomials

Abstract

Keywords

Cite

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