Average number of squares dividing mn

Abstract

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.

12 pages, 1 figure

Cited by in corpus (1)

• On multivariable averages of divisor functions