Maximal height of divisors of $x\sp n-1$

Abstract

The size of the coefficients of cyclotomic polynomials is a problem that has been well-studied. This paper investigates the following generalization: suppose $f(x)\in\mathbb{Z}[x]$ is a divisor of $x^n-1$, so that $f(x)$ is the product of the cyclotomic polynomials corresponding to some of the divisors of $n$. We ask about the largest coefficient in absolute value over all such divisors $f(x)$ of $x^n-1$, obtaining a fairly tight estimate for the maximal order of this function.