Abstract
Let $\mathbf{a}=(a_1,\cdots,a_k)$ denote a $k$-tuple of positive integers such that $a_1 \leq a_2 \leq\break \cdots \leq a_k$. We put $d(\mathbf{a};n)=\sum_{n_1^{a_1}\cdots n_k^{a_k}=n}1$ and let $\Delta(\mathbf{a};x)$ be the error term of the corresponding asymptotic formula for the summatory function of $d(\mathbf{a};n)$. In this paper we show an asymptotic formula of the mean square of $\Delta(\mathbf{a};x)$ under a certain condition. Moreover, when $k$ equals $2$ or $3$, we give unconditional asymptotic formulas for these mean squares.
Citation
Xiaodon Cao. Yoshio Tanigawa. Wenguang Zhai. "Mean square of the error term in the asymmetric multidimensional divisor problem." Funct. Approx. Comment. Math. 54 (2) 173 - 193, June 2016. https://doi.org/10.7169/facm/2016.54.2.4
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