Abstract
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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