Resultants of cyclotomic polynomials

Abstract

where the 'indicates that the index k runs through integers relatively prime to n. The degree of Fn(x) is +(n), Euler's totient. This paper determines the resultant p(Fm, Fn) of any two cyclotomic polynomials Fm and Fn. Explicit formulas are given which show that if m$n the resultant is either 1, -2, or a prime power. For the case m > n > 1 the results agree with a formula derived by Diederichsen [3, Hilfssatz 2] in a paper on group representations (see Theorem 4 below). Our proof is different from and somewhat simpler than that of Diederichsen; it is based on the following lemma on decompositions of reduced residue systems which the author has recently used to relate Gauss sums and primitive characters [1, Lemma 6].