An introduction to decoupling and harmonic analysis over 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 Q p \mathbb {Q}_p . Over Q p \mathbb {Q}_p , commonly used heuristics in decoupling are significantly easier to make rigorous over Q p \mathbb {Q}_p than over R \mathbb {R} and such decoupling theorems over Q p \mathbb {Q}_p are still strong enough to derive interesting number theoretic conclusions.