论文标题

超过$ \ mathbb {q} _p $的去耦和谐波分析简介

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

论文作者

Li, Zane Kun

论文摘要

该说明性论文的目的是通过在抛物线的更简单的解耦设置上进行介绍,以超过$ \ mathbb {q} _p $。超过$ \ mathbb {q} _p $,与$ \ mathbb {q} _p $相比,与$ \ mathbb {r} $相比,与$ \ mathbb {q} _p $相比,通常使用的启发式方法要容易得多。

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.

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