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 $$|\widehat{1_A}|<em>1\geq (c</em>\mathcal{R}-o_{|A| \rightarrow \infty}(1))\sqrt{|A|}$$ where $c_\mathcal{R}=0.953\dots$.