Gowers uniformity norms

[YaelDillies]

Given $f : G \to \mathbb C$ with $G$ finite abelian, one can define its $U^2$-norm by
$$||f||_{U^2} = \mathbb E _{x, a, b} f(x) \overline{f(x + a) f(x + b)} f(x + a + b)$$

It would be great to straight away have a definition of $U_{2^n}$ for all $n$.

This is Definition 4.5 in the lecture notes.