Writing $\widehat G$ for the <character group of a finite abelian group>, the <Bohr set> with frequency set $\Gamma\subseteq\widehat G$ and width $0\leq\rho\leq2$ is
$$
B(\Gamma,\rho)
=\{x\in G:|\gamma(x)-1|\leq\rho\text{ for every }\gamma\in\Gamma\}.
$$
Its rank is $|\Gamma|$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 129 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-129/2/a/solution