Cyclotomic properties of polynomials associated with automatic sequences
Number Theory
2019-09-30 v2
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.
Cite
@article{arxiv.1909.12052,
title = {Cyclotomic properties of polynomials associated with automatic sequences},
author = {Bartosz Sobolewski},
journal= {arXiv preprint arXiv:1909.12052},
year = {2019}
}
Comments
19 pages, 4 figures; typos corrected