Salem numbers from a class of star-like trees

Abstract

We study the Coxeter polynomials associated with certain star-like trees. In particular, we exhibit large Salem factors of these polynomials and give convergence properties of their dominant roots.Comment: 10 page

Seventy years of Salem numbers

“…A second method is to use results of Mann [72] on sums of roots of unity. This method was used by Gross, Hironaka and McMullen [47] for polynomials coming from modified Coxeter diagrams, and by Brunotte and Thuswaldner [27] for polynomials coming from star-like trees.…”