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arXiv · 2211.07086

Totally real algebraic integers in short intervals, Jacobi polynomials, and unicritical families in arithmetic dynamics

Chatchai Noytaptim·Clayton Petsche
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Abstract

We classify all post-critically finite unicritical polynomials defined over the maximal totally real algebraic extension of ${\mathbb Q}$. Two auxiliary results used in the proof of this result may be of some independent interest. The first is a recursion formula for the $n$-diameter of an interval, which uses properties of Jacobi polynomials. The second is a numerical criterion which allows one to the give a bound on the degree of any algebraic integer having all of its complex embeddings in a real interval of length less than $4$.

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Chatchai Noytaptim, Clayton Petsche. 2022-11-14. Totally real algebraic integers in short intervals, Jacobi polynomials, and unicritical families in arithmetic dynamics. https://arxiv.org/abs/2211.07086

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