Valeriya Kovaleva (Université de Montréal)

Statistics of the divisor function on intervals (y,2y]

For a random integer n, $\tau(n;y)$, the number of divisors of n in the interval (y,2y], is also a random variable. In 2009 Ford showed that $\tau(n;y)$ is non-zero less often than expected heuristically due to a profound structural phenomenon affecting divisors of $n$. Other than that, little is known about the distribution of $\tau(n;y)$. We present several results aimed at understanding this distribution and discuss the connection with sums of random multiplicative functions. This is work in progress.