## Functiones et Approximatio Commentarii Mathematici

### A generalized divisor problem and the sum of Chowla and Walum II

#### 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.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 49, Number 1 (2013), 159-188.

Dates
First available in Project Euclid: 20 September 2013

https://projecteuclid.org/euclid.facm/1379686440

Digital Object Identifier
doi:10.7169/facm/2013.49.1.10

Mathematical Reviews number (MathSciNet)
MR3003959

Zentralblatt MATH identifier
1293.11097

Subjects
Primary: 11N37: Asymptotic results on arithmetic functions

#### Citation

Cao, Xiaodong; Furuya, Jun; Tanigawa, Yoshio; Zhai, Wenguang. A generalized divisor problem and the sum of Chowla and Walum II. Funct. Approx. Comment. Math. 49 (2013), no. 1, 159--188. doi:10.7169/facm/2013.49.1.10. https://projecteuclid.org/euclid.facm/1379686440

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