Solution
= Solution
With normalized averages on the finite abelian group $G$, the <Gowers U2 norm> is defined by
$$
\|f\|_{U^2}^4
=\mathbb E_{x,a,b}f(x)\overline{f(x+a)}\,\overline{f(x+b)}f(x+a+b).
$$
The <Gowers U3 norm> is defined by
$$
\|f\|_{U^3}^8
=\mathbb E_{x,a,b,c}
\prod_{\epsilon\in\{0,1\}^3}
\mathcal C^{|\epsilon|}f(x+\epsilon_1a+\epsilon_2b+\epsilon_3c),
$$
where $\mathcal C$ denotes complex conjugation.