Abstract
In this paper, we study the relation between the discrete and the continuous mean values of $\Delta_a^2(x)$, where $\Delta_a(x)$ $(-1<a<1)$ is the error term in the generalized divisor problem. We try to find the formula of the difference of these mean values in a sufficiently explicit form. As an application we give the asymptotic formula of the discrete mean square of $\Delta_a(n)$ in the range $-1<a<1, a\not=0$. We also study the integral containing the error term in the weighted two-dimensional divisor problem.
Citation
Xiaodong Cao. Jun Furuya. Yoshio Tanigawa. Wenguang Zhai. "A generalized divisor problem and the sum of Chowla and Walum II." Funct. Approx. Comment. Math. 49 (1) 159 - 188, September 2013. https://doi.org/10.7169/facm/2013.49.1.10
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