TOWARDS A CLASSIFICATION OF REGULAR SEQUENCES (Analytic Number Theory and Related Topics)

Abstract

In the mid-2000s, Adamczewski and Buguead proved the CobhamLoxton-van der Poorten conjecture by using the subspace theorem to show that any automatic number (a number whose base expansion is given by an automatic sequence) is either rational or transcendental. About 10 years later, again using the subspace theorem, Bell, Bugeaud, and Coons, extended this result to regular sequences-the (possibly unbounded) generalization of automatic sequences. In this survey, we discuss a further characterization of regular sequences by defining an associated measure, the so-called ghost measure, which is governed by the underlying properties of a related finite set of matrices.