= Gowers U3 norm on an interval
{c}
{title2=$\|f\|_{U^3(N)}$}
= Interval Gowers U3 norm
{synonym}
Normalize the conjugated cube average by the number of integer cubes whose vertices all lie in the interval. Equivalently, extend $f$ by zero to a cyclic group of order greater than $8N$ and divide its <Gowers U3 norm> by that of the interval's <indicator function>. A <quadratic phase> then has norm one. Omitting the denominator gives a different but uniformly equivalent interval normalization.
Back to article page
