 Gowers U3 norm

ID: gowers-u3-norm

The third Gowers norm is the eighth root of the conjugated product around a three-dimensional affine cube:

∥ f ∥_{U^{3}}^{8} = E_{x, a, b, c} \prod_{ϵ \in {0, 1}^{3}} C^{∣ ϵ ∣} f (x + ϵ_{1} a + ϵ_{2} b + ϵ_{3} c) .

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