Uniform bounds on $S$-integral preperiodic points for chebyshev polynomials

Abstract

Let $K$ be a number field with algebraic closure $\bar{K}$, let $S$ be a finite set of places of $K$ containing the archimedean places, and let $\ddot{I}†$ be Chebyshev polynomial. In this paper we prove uniformity results on the number of $S$-integral preperiodic points relative to a non-preperiodic point ${\hat{I}}^2$, as ${\hat{I}}^2$ varies over number fields of bounded degree.

14 pages. arXiv admin note: text overlap with arXiv:2302.01562, arXiv:0808.2679, arXiv:0805.1554 by other authors