Geodesic
On the Dedekind zeta function
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 184-197

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Let $K_n$ be a number field of degree $n$ over $\mathbb Q$. Denote by $A_{K_n}(x)$ the number of ideal with norm $\leq x$. Landau's classical estimate is $$ A_{K_n}(x)=\Lambda_nx+O(x^{(n-1)/(n+1)}). $$ In this paper the error term is improved for the non-normal field $K_4=\mathbb Q(\root4\of m)$ and for $K_6$, the normal closure of a cubic field $K_3$ with the Galois group $S_3$. 
@article{ZNSL_2013_418_a12,
     author = {O. M. Fomenko},
     title = {On the {Dedekind} zeta function},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {184--197},
     publisher = {mathdoc},
     volume = {418},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a12/}
}
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O. M. Fomenko. On the Dedekind zeta function. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 184-197. http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a12/