English

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.

Keywords

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

R2 v1 2026-06-23T11:26:48.072Z