Andrew V. Lelechenko
Published 2014-07-04, updated 2014-12-08Version 2
We study the asymptotic behaviour of $\sum_{m,n\le x} \tau_{1,2}(mn)$, where $\tau_{1,2}(n) = \sum_{a b^2 = n} 1$, using multidimensional Perron formula and complex integration method. An asymptotic formula with an error term $O(x^{10/7})$ is obtained.
Comments: 12 pages, 1 figure
Journal: Visn. Odessk. Univ., Ser. Mat. Mekh., 2014, vol. 19, #2 (22), p. 52-65
On asymptotic behaviour of Dirichlet inverse
On the average number of subgroups of the group $\Z_m \times \Z_n$
On the weighted average number of subgroups of ${\mathbb {Z}}_{m}\times {\mathbb {Z}}_{n}$ with $mn\leq x$
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