We prove that sums of the form with f(X), g(X) ∈ ℤ[X] can be explicitly computed whenever f and g are subject to some certain conditions which are defined in the paper.
Let p be an odd prime such that the Greenberg conjecture holds for the maximal real cyclotomic subfield K1 of Q[ζp]. Let An = (C(Kn))p be the p-part of the class group of Kn, the n-th field in the cyclotomic tower, and let En, Cn be the global and cyclotomic units of Kn, respectively. We prove that under this premise, there is some n0 such that for all m ≥ n0, the class number formula (Em/Cm)p = |Am| hides in fact an isomorphism of Λ[Gal(K1/Q)]-modules.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.