On the error term for the sum of the coefficients of Dedekind zeta-function over square numbers. (English) Zbl 1399.11161
Summary: Suppose that \(E\) is an algebraic number field over the rational field \(\mathbb{Q}\). Let \(a\left(n \right)\) be the number of integral ideals in \(E\) with norm \(n\). Let also \(\Delta \left(x \right)\) denote the remainder term in the asymptotic formula for the average behavior \({\sum_{n \leq x}}{\left({a\left({{n^2}} \right)} \right)^l}\). In this paper, the sharp bound for
\[
\int_1^X {{\Delta ^2}\left(x \right){\text{dx}}}
\]
is given by analytical method.
MSC:
11N37 | Asymptotic results on arithmetic functions |
11R42 | Zeta functions and \(L\)-functions of number fields |