Maximal height of divisors of $x^{pq^{b}}-1$

Abstract

The height of a polynomial $f(x)$ is the largest coefficient of $f(x)$ in absolute value. Let B(n) be the largest height of a polynomial in $\mathbb{Z}[x]$ dividing $x^n-1$. In this paper we investigate the maximal height of divisors of $x^{pq^b}-1$ and prove that some conjectures on the maximal height of divisors of $x^{pq^b}-1$ are true.