Divisors of an Integer in a Short Interval

Abstract

Let ${\mathcal{D}}_n\subset \mathbb{N}$ denote the set of the $\ddot{I}„(n)$ divisors of $n$. We study the function $$D_n(X,Y):=|\{d\in {\mathcal{D}}_n:X\le d\le X+Y\}|$$ for $Y\le X$.