The Wiener norm of lifts of dense Sidon sets

Abstract

We describe, with proof, an infinite class of examples of finite sets of integers $A$ for which $\|\widehat{1_A}\|_1\geq (c_\mathcal{R}-o_{|A| \rightarrow \infty}(1))\sqrt{|A|}$ where $c_\mathcal{R}=0.953\dots$.