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Critical Point Criteria and Dynamically Monogenic Polynomials by König, Joachim; Smith, Hanson; Wolske, Zack is a scholarly article available to read on EtoBox.

What is Critical Point Criteria and Dynamically Monogenic Polynomials about?

Let $K$ be a number field with ring of integers $\mathcal{O}_K$, and let $f(x)\in\mathcal{O}_K[x]$ be a monic, irreducible polynomial. We establish necessary and sufficient conditions in terms of the critical points of $f(x)$ for the iterates of $f(x)$ to be monogenic polynomials. More generally, we give necessary and sufficient conditions for the backwards orbits of elements of $\mathcal{O}_K$ under $f(x)$ to be monogenerators. We apply our criteria to construct novel examples of dynamically monogenic polynomials, yielding infinite towers of monogenic number fields with the backward orbit of one monogenerator giving a monogenerator at the next level.

Author

König, Joachim; Smith, Hanson; Wolske, Zack

Published

2024

Language

EN