On the number of integral ideals in galois extensions

Abstract

If a k denotes the number of integral ideals with normk, in any finite Galois extension of the rationals, we study sums of the form Σ_k≤x a^l_k (l = 2,3, ...) "align="middle" border="0"> , along with the integral means of the 2ρ-th power (ρ real,ρ ≥1) of the absolute value of the corresponding Dedekind zeta-function. The two averages are related if ρ=n^1-1/2, wheren is the degree of the Galois extension.