Geodesic
On the Dedekind zeta function. II
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 178-192 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $K_n$ be a number field of degree $n$ over $\mathbb Q$. Denote by $A(x,K_n)$ the number of integer ideals of $K_n$ with norm $\leq x$. For $K_8=\mathbb Q(\sqrt{-1},\root4\of m)$, $K_8=\mathbb Q(\root4\of{\varepsilon_m})$ and $K_{16}=\mathbb Q(\sqrt{-1},\root4\of{\varepsilon_m})$, where $m$ is a positive square free integer and $\varepsilon_m$ denotes the fundamental unit of $\mathbb Q(\sqrt m)$, the author proves that $$ A(x,K_n)=\Lambda_nx+\Delta(x,K_n)(x,K_n),\quad\Delta(x,K_n)\ll x^{1-\frac3{n+2}+\varepsilon}. $$ This improves earlier results of E. Landau (1917) and W. G. Nowak (Math. Nachr. 161 (1993), 59–74) for the indicated special cases. The author also treats Titchmarch's phenomenon for $\zeta_{K_n}(s)$ and large values of $\Delta(x,K_n)$. 
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     title = {On the {Dedekind} zeta {function.~II}},
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O. M. Fomenko. On the Dedekind zeta function. II. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 178-192. http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a12/

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