Bounds for the maximal height of divisors of xn−1

AbstractTextThe problem of determining the maximum size of coefficients of cyclotomic polynomials has been studied extensively. Let A(n) be the maximum absolute value of a coefficient of Φn(x), the nth cyclotomic polynomial. This paper further investigates a variation of A(n) introduced by Pomerance and Ryan. We consider the function B(n), the maximum absolute value of a coefficient of any divisor of xn−1. In the first part of this paper we give an analogue of a well-known result for A(n) proved independently by Felsch and Schmidt, and by Justin, and give an upper bound for B(n) for a general n. In the second part of the paper we resolve a question of Pomerance and Ryan giving an explicit formula for B(p2q). We then give upper and lower bounds for B(pqr) where p<q