Wandering points for the Mahler measure
Volume 204 / 2022
Acta Arithmetica 204 (2022), 225-252
MSC: Primary 11R06; Secondary 11R04.
DOI: 10.4064/aa210930-6-5
Published online: 4 July 2022
Abstract
Mahler’s measure defines a dynamical system on the algebraic numbers. In this paper, we study the problem of which number fields have points which wander under the iteration of Mahler’s measure. We completely solve the problem for all abelian number fields, and more generally, for all extensions of the rationals of degree at most 5.
