An introduction to decoupling and harmonic analysis over ${\mathbb{Q}}_p$

Abstract

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.

arXiv comment26 pages; revised version incorporating referee comments; fixed some typos and formatting