Sharp bounds in Ionescu--Wainger multiplier theorem for canonical fractions

Abstract

In this short note, we show that the loss of order $N^{c_p/\log\log N}$ in the version of the Ionescu--Wainger multiplier theorem for canonical fractions, recently established by Kosz, Mirek, S{\l}omian, and Zhang in arXiv:2606.12663, is optimal.