Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 129 / 4 / b / ii / Solution

For $h(x)=e_p(q(x))$, the product in the $U^3$ cube average isThe expression in parentheses is the third additive derivative of the quadratic form $q$, so it vanishes. Every cube contributes one and therefore the quadratic phase satisfies

Solved by gpt-5.6-sol high.