Gaps in Multiplicative Sidon Sets II

Abstract

With $\ddot{I}=\frac{13-\sqrt{69}}{10}\approx 0.47$, it was recently established that there exist multiplicative Sidon sets (sets without any non-trivial solutions to $ab=cd$) in $\{1,2,\dots ,n\}$ with maximal gap size ${\ll }_{\epsilon }{n}^{\ddot{I}+\epsilon }$. Here we improve upon this result and show that one can take $\ddot{I}=\frac{10}{33}\approx 0.303$ instead.

6 pages