Cyclotomic properties of polynomials associated with automatic sequences

2019/09/26 by Sobolewski, Bartosz
#11B85 (Primary) 11B37 #11C08 #11R18 #68Q45 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.12052

Abstract

We show that polynomials associated with automatic sequences satisfy a certain recurrence relation when evaluated at a root of unity, which generalizes a result of Brillhart, Lomont and Morton on the Rudin--Shapiro polynomials. We study the minimal order of such a relation and the integrality of its coefficients.

Related

• On a sequence of polynomials with hypothetically integer coefficients
• A Survey on Coefficients of Cyclotomic Polynomials
• Cyclotomic ordering conjecture
• Enumeration and Decidable Properties of Automatic Sequences
• Factors of generalised polynomials and automatic sequences