Cyclotomic properties of polynomials associated with automatic sequences
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.
19 pages, 4 figures; typos corrected