有限域上某些多项式族的动态不可约性

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-06-12 DOI:10.1016/j.ffa.2025.102666

Tori Day , Rebecca DeLand , Jamie Juul , Cigole Thomas , Bianca Thompson , Bella Tobin

引用次数: 0

摘要

给出了共轭于h(x)=axd+c的单临界多项式在有限域上动态不可约的充分必要条件。这一结果推广了Boston-Jones和Hamblen-Jones-Madhu关于特定单临界多项式族的动态不可约性的结果。我们还研究了三次线性化多项式和移位线性化多项式的动态不可约条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dynamical irreducibility of certain families of polynomials over finite fields

We determine necessary and sufficient conditions for unicritical polynomials conjugate to

h (x) = a x^{d} + c

to be dynamically irreducible over finite fields. This result extends the results of Boston-Jones and Hamblen-Jones-Madhu regarding the dynamical irreducibility of particular families of unicritical polynomials. We also investigate dynamical irreducibility conditions for cubic and shifted linearized polynomials.

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.