Finding Almost Squares

Abstract

We study short intervals which contain an ``almost square'', an integer $n$ that can be factored as $n=ab$ with $a$, $b$ close to $\sqrt{n}$. This is related to the problem on distribution of $n^2\alpha (\mathrm{mod}1)$ and the problem on gaps between sums of two squares.

12 pages, report number added

Cited by in corpus (2)

• Next Order Asymptotics and Renormalized Energy for Riesz Interactions
• Distance between arithmetic progressions and perfect squares