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On the Dedekind Zeta Function

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Let Kn be a number field of degree n over Q. By \( {A}_{K_n}(x) \) denote the number of integral ideals with norm ≤ x. Landau’s classical estimate is

$$ {A}_{K_n}(x)={\varLambda}_n x+ O\left({x}^{\left( n-1\right)/\left( n+1\right)}\right). $$

In this paper, the error term is improved for the non-normal field \( {K}_4=\mathrm{Q}\left(\sqrt[4]{m}\right) \) and for K6, the normal closure of a cubic field K3 with the Galois group S3. Bibliography: 25 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. 418, 2013, pp. 184–197.

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Fomenko, O.M. On the Dedekind Zeta Function. J Math Sci 200, 624–631 (2014). https://doi.org/10.1007/s10958-014-1952-6

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