Maximum gap in (inverse) cyclotomic polynomial

Cyclotomic coefficients: gaps and jumps

“…Recently, there has been a burst of activity in studying the cyclotomic coefficients a n (k), see, for example, [3,4,5,6,10,15,17,18,19,31,35] and references therein. Furthermore, in several works inverse cyclotomic polynomials Ψ n (Z) = (Z n − 1)/Φ n (Z) have also been considered, see [7,21,22,23,29]. The identities Φ 2n (Z) = Φ n (−Z), with n > 1 odd and Φ pm (Z) = Φ m (Z p ) if p | m, show that, as far as the study of coefficients is concerned, the complexity of Φ n (Z) is determined by its number of distinct odd prime factors.…”

A Note on Ternary Cyclotomic Polynomials

“…There are also papers on the coefficients of inverse cyclotomic polynomials (see Moree [12], Bzdȩga [3]) and on maximum gap in (inverse) cyclotomic polynomials (see Hong, Lee, Lee and Park [6]). …”

Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers

“…Hong et al [9] studied g(Φ n ) (inspired by a cryptographic application [10]). They reduce the study of these gaps to the case where n is square-free and odd and established the following result for the simplest non-trivial case.…”