  The goal of this expository paper is to provide an introduction to decoupling
by working in the simpler setting of decoupling for the parabola over
$\mathbb{Q}_p$. Over $\mathbb{Q}_p$, commonly used heuristics in decoupling are
significantly easier to make rigorous over $\mathbb{Q}_p$ than over
$\mathbb{R}$ and such decoupling theorems over $\mathbb{Q}_p$ are still strong
enough to derive interesting number theoretic conclusions.

Number Theory;Classical Analysis and ODEs