We study an asymptotic behavior of the sum $\sum\limits_{n\le x}\frac{\D \tau(n)}{\D \tau(n+a)}$. Here $\tau(n)$ denotes the number of divisors of $n$ and $a\ge 1$ is a fixed integer.
On the mean square of the divisor function in short intervals
On an asymptotic behavior of the divisor function $τ(n)$
The Mean Square of Divisor Function
![QR code for arXiv:1011.1391 [math.NT]](http://oss.arxitics.com/images/favicon.svg)