Higher-order Fourier analysis of ${\mathbb{F}}_p^n$ and the complexity of systems of linear forms

Hamed Hatami, Shachar Lovett

Consider a subset $A$ of ${\mathbb{F}}_p^n$ and a decomposition of its indicator function as the sum of two bounded functions $1_A=f_1+f_2$. For every family of linear forms, we find…