Salem numbers from a class of star-like trees

TL;DR

This paper investigates Coxeter polynomials of specific star-like trees, revealing large Salem factors and analyzing the convergence behavior of their dominant roots, contributing to the understanding of algebraic integers related to these structures.

Contribution

It introduces new results on Salem factors of Coxeter polynomials for star-like trees and studies the convergence of their dominant roots.

Findings

Identification of large Salem factors in Coxeter polynomials.

Analysis of convergence properties of dominant roots.

Enhanced understanding of algebraic integers from 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.