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Mean values connected with the Dedekind zeta function

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Abstract

For a cubic extension K3/ℚ, which is not normal, new results on the behavior of mean values of the Dedekind zeta function of the field K3 in the critical strip are obtained.

Let M(m) denote the number of integral ideals of the field K3 of norm m. For the sums

$$\sum\limits_{m \leqslant x} {M(m)^2 } and \sum\limits_{m \leqslant x} {M(m)^3 } $$

asymptotic formulas are derived. Previously, only upper bounds for these sums were known. Bibliography: 23 titles.

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  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    O. M. Fomenko

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Correspondence to O. M. Fomenko.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 350, 2007, pp. 187–198.

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Fomenko, O.M. Mean values connected with the Dedekind zeta function. J Math Sci 150, 2115–2122 (2008). https://doi.org/10.1007/s10958-008-0126-9

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