Finding Almost Squares VII
Department
Mathematics
Document Type
Article
Publication Date
1-1-2022
Abstract
A positive integer n is called an almost square of type 2 if it can be factored in two different ways as n = a1b1 = a2b2 with a1, a2, b1, b2 ≈√n. We are interested in how short an interval around x, say [x − xϕ, x + xϕ], contains such kinds of integers. In this note, we improve upon previous upper bounds on ϕ using exponential sum techniques including recent breakthroughs on Vinogradov’s mean value theorem.
Journal Title
Integers
Volume
22
Digital Object Identifier (DOI)
NA
COinS