Monogenic Cyclotomic compositions

Abstract

Let m and n be positive integers, and let p be a prime. Let T(x) = Φ_p^m (Φ_2ⁿ(x)), where Φ_k(x) is the cyclotomic polynomial of index k. In this article, we prove that T(x) is irreducible over Q and that

       {1, θ, θ², ..., θ^{2n-1pm-1(p-1)-1}}

is a basis for the ring of integers of Q(θ), where T(θ) = 0.