有限域上多项式某些族的动态不可约性

arXiv - MATH - Number Theory Pub Date : 2024-09-16 DOI:arxiv-2409.10467

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

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引用次数: 0

摘要

我们确定了单临界多项式在有限域上动态不可约的必要条件和充分条件。这一结果扩展了 Boston-Jones 和 Hamblen-Jones-Madhu 关于单临界多项式特定族的动态不可还原性的结果。我们还研究了三次多项式和移位线性化多项式的动态不可还原性条件。

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Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields

We determine necessary and sufficient conditions for unicritical polynomials 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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arXiv - MATH - Number Theory

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