A note on product sets of rationals

TL;DR

This paper improves a lower bound on the size of the product set of rational numbers with bounded numerator and denominator, using a novel approach to extend previous results by Bourgain, Konyagin, and Shparlinski.

Contribution

It introduces a new method to slightly enhance the lower bound for the product set size of rationals with bounded numerator and denominator.

Findings

Enhanced lower bound for product set size

New approach improves previous results

Applicable to sets of rationals with bounded numerator and denominator

Abstract

Bourgain, Konyagin and Shparlinski obtained a lower bound for the size of the product set AB when A and B are sets of positive rational numbers with numerator and denominator less or equal than Q. We extend and slightly improve that lower bound using a different approach.