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

Abstract

AbstractWe classify all postcritically finite unicritical polynomials defined over the maximal totally real algebraic extension of . Two auxiliary results used in the proof of this result may be of some independent interest. The first is a recursion formula for the diameter of an interval, which uses properties of Jacobi polynomials. The second is a numerical criterion that allows one to 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.