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On the factorization of iterated polynomials
Revista Matemática Iberoamericana ( IF 1.3 ) Pub Date : 2020-03-16 , DOI: 10.4171/rmi/1187
Lucas Reis 1
Affiliation  

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).

中文翻译:

关于迭代多项式的因式分解

令$ \ mathbb {F} _q $是具有$ q $元素的有限域,并且$ f,\ mathbb {F} _q [x] $中的g \是度数至少为1的多项式。本文讨论了与$ \ mathbb {F} _q $上的迭代多项式$ f(g ^ {(n)}(x))$的因式分解相关的某些算术函数的渐近增长,例如最大程度的不可约因子和不可约因子的数量。特别是,我们对D.Gómez-Pérez,A。Ostafe和I. Shparlinski(2014)的结果进行了重大改进。
更新日期:2020-03-16
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