The Automatic Study of Constant Term Sequences Modulo Prime Powers

Abstract

In this thesis, we examine integer sequences arising as coefficients of the powers of a multivariate Laurent polynomial. We provide multiple motivations for studying these sequences, and in particular, we focus on their prime power residues as a special class of automatic sequences. We use this perspective to study the frequencies of residues in these sequences and classify the constant term sequences modulo prime powers that are uniformly recurrent.