Abstract
Ifa k denotes the number of integral ideals with normk, in any finite Galois extension of the rationals, we study sums of the form\(\sum\limits_{k \leqslant x} {a_k^l } (l = 2,3, \ldots )\), 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.
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Chandrasekharan, K., Good, A. On the number of integral ideals in Galois extensions. Monatshefte für Mathematik 95, 99–109 (1983). https://doi.org/10.1007/BF01323653
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DOI: https://doi.org/10.1007/BF01323653