On the variance of sums of divisor functions in short intervals

Stephen Lester

paper

On the variance of sums of divisor functions in short intervals

arXiv:1502.01170

Abstract

Given a positive integer $n$ the $k$ -fold divisor function $d_{k} (n)$ equals the number of ordered $k$ -tuples of positive integers whose product equals $n$ . In this article we study the variance of sums of $d_{k} (n)$ in short intervals and establish asymptotic formulas for the variance of sums of $d_{k} (n)$ in short intervals of certain lengths for $k = 3$ and for $k \geq 4$ under the assumption of the Lindelöf hypothesis.

13 pages