Difference sets and positive exponential sums. II: Cubic residues in cyclic groups (Q2234367)

Let \(q\) be a (composite) number and consider a set \(A \subseteq \mathbb{Z}/q\mathbb{Z}\) such that \(A-A\) avoids the set of cubic residues modulo \(q\). In the paper under review the authors obtain the bound \(|A| = O_\varepsilon (q^{1/2+\varepsilon})\). The proof uses some constructions of suitable nonnegative exponential sums. For Part I see [J. Fourier Anal. Appl. 20, No. 1, 17--41 (2014; Zbl 1354.11017)].