Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 129 / 2 / i / Solution

Use normalized Fourier analysis on a finite abelian group. If $A\subseteq {\mathbb{F}}_2^n$ has density $\alpha$, its large spectrum at level $\rho >0$ isThe Chang theorem states that this spectrum is contained in a subspace of dimensionEquivalently, it is contained in the span of a dissociated set of that size.